化學

氫原子光譜與波耳氫原子模型

氫原子光譜與芮得柏方程式

光的波動性

• 光為電磁波，在真空中以
  $3\times {10}^{8}m/s$ 的速度前進(化學先不要考慮介質)
• 電磁波的
  $\lambda (\mathrm{波}\mathrm{長})、\nu (\mathrm{頻}\mathrm{率})、c(\mathrm{波}\mathrm{速})$三者關係如下:
  $$c(\mathrm{波}\mathrm{速})=\nu (\mathrm{頻}\mathrm{率})\times \lambda (\mathrm{波}\mathrm{長})(c:3\times {10}^{8}m/s，\nu :s^{-1}，\lambda :m)$$

單位有:

$1nm={10}^{-9}m\mathrm{和}1\mathring{A}={10}^{-10}m$
頻率排名:

$\gamma \mathrm{射}\mathrm{線}>X\mathrm{射}\mathrm{線}>\mathrm{紫}\mathrm{外}\mathrm{線}>\mathrm{可}\mathrm{見}\mathrm{光}>\mathrm{紅}\mathrm{外}\mathrm{線}>\mathrm{微}\mathrm{波}>\mathrm{無}\mathrm{線}\mathrm{電}\mathrm{波}$
可見光波長範圍大概在 400奈米~700奈米左右

---

光的粒子性

-普朗克提出光的能量和頻率成正比
-愛因斯坦認為光具有粒子的性質，稱為光子

$$E=h\times \nu =\frac{h\times c}{\lambda }\{\begin{array}{l}E:\mathrm{光}\mathrm{能}(\mathrm{一}\mathrm{個}\mathrm{光}\mathrm{子}\mathrm{的}\mathrm{能}\mathrm{量})\\ h:\mathrm{普}\mathrm{朗}\mathrm{克}\mathrm{常}\mathrm{數}=6.626\times {10}^{-34}\mathrm{焦}\mathrm{耳}\cdot \mathrm{秒}/\mathrm{每}\mathrm{個}\mathrm{光}\mathrm{子}\end{array}$$

$E(\mathrm{光}\mathrm{能})\propto \nu \propto \frac{1}{\lambda }$

---

氫原子光譜

-為不連續的明線光譜，每一條譜線都對應一條特定頻率、波長的光
-光譜可分為三塊:紫外光區、可見光區、紅外光區
-每塊的線之間的間隔有規律性，各相鄰光譜線之間隨著頻率增加而越來越近

---

芮得柏方程式

1885年，瑞士數學老師巴耳末找到氫原子光譜可見光區前4條譜線波長的經驗公式

$$\lambda ={\lambda }_0\times \frac{n^2}{n^2-4}{\lambda }_0=364.6nm，n=3、4、5、......$$

• 科學家因為受到巴耳末經驗公式的啟發，逐漸去探討到紫外光區與紅外光區，美國來曼、德國帕申分別在紫外光區、紅外光區發現一組譜線
• 1889年瑞典物理科學家芮得柏提出氫原子譜線的經驗公式:
  
  $$\frac{1}{\lambda }=R_H\times (\frac{1}{{n_1}^2}-\frac{1}{{n_2}^2})$$
  
  $R_H(\mathrm{芮}\mathrm{得}\mathrm{柏}\mathrm{常}\mathrm{數})=1.097\times {10}^{-2}n{m}^{-1}，n_1、n_2\mathrm{為}\mathrm{正}\mathrm{整}\mathrm{數}\mathrm{且}{n}_2>n_1$

芮得柏方程式只是經驗公式，芮得柏未能深入研究這一公式其中的物理意義。直到1913年丹麥物理學家波耳創立了波耳模型，芮得柏方程式的物理意義才得到合理的解釋

---

波耳的氫原子學說

因拉塞福原子模型有兩個問題

$$\begin{array}{rl}& \text{1. 不能解釋原子之穩定性：}\\ & \because \text{電子繞核作高速圓周運動時，必因加速而有電磁輻射放出，電子能量急速減少，}\\ & \text{必會循螺線型趨向原子核，直至墜入核中而崩潰，事實不然，氫原子相當穩定。}\\ & \text{2. 不能解釋明線之原子光譜：}\\ & \because \text{當電子輻射能量而逐漸接近原子核時，應放出頻率越來越高的電磁波而產生連續光譜，}\\ & \text{但事實上氫原子為明線光譜。}\end{array}$$

• 波耳為了解釋氫原子的穩定性與原子光譜，他留了行星模型，波耳認為電子有如行星般圍繞原子核運轉，其向心力源於電子核與原子核之間的庫倫作用力。

---

波耳在古典物理法則加入以下兩個假設。

1. 第一假設:

   1. 氫原子的電子只在特定半徑的圓形軌道上運動。當電子在這些軌道以外的地方運行時。電子將不在輻射能量亦不吸收能量而成穩定態，這些軌道自原子核由內而外分別以
      $n=1、2、3、4、5、.......、\mathrm{\infty }$等表示。
   2. 在軌道上運動的電子，都具有一定的能量，這些能量的高低以能階表示。
      波耳計算出氫原子電子在第
      $n$個軌道上的能量為
      $E_n$。
      $$E_n=-\frac{k}{n^2}k=1312kj/mol，2.179\times {10}^{-18}J/\mathrm{每}\mathrm{個}\mathrm{電}\mathrm{子}$$

      1. $n=1$的軌道最靠近原子核，半徑最小，能量最低，稱為基態。
      2. $n$越大，軌道離原子核愈遠，半徑愈大，能量越高，
         $n>1$的能量高於基態，稱為激發態。

   ---

2. 第二假設:

   1. 在基態
      $(n=1)$的電子吸收能量後，能夠躍遷至較高能階，其吸收的能量等於兩能階的能量差。
   2. 當電子由一個較高能階
      $(E_H)$躍遷至較低能階
      $(E_L)$時，電子會將兩能階的能量差以電磁波的形式放出而產生光譜。
      
      $$\begin{array}{rl}& \mathrm{\Delta }E=E_H-E_L=(\frac{-k}{{n_H}^2})-(\frac{-k}{{n_L}^2})=k(\frac{1}{{n_L}^2}-\frac{1}{{n_H}^2})\\ & \nu =\frac{k}{h}(\frac{1}{{n_L}^2}-\frac{1}{{n_H}^2})=R(\frac{1}{{n_L}^2}-\frac{1}{{n_H}^2})\\ & R(\mathrm{芮}\mathrm{得}\mathrm{柏}\mathrm{常}\mathrm{數})=3.29\times {10}^{15}{s}^{-1}\\ & \lambda =\frac{c}{\nu }=\frac{c}{R}\times \frac{1}{(\frac{1}{{n_L}^2}-\frac{1}{{n_H}^2})}\end{array}$$

---

氫原子光譜系列:

1. 來曼系列(紫外光區) :電子由
   $n>1$降至
   $n=1$所產生的光譜。
2. 巴耳末系列(可見光區):電子由
   $n>2$降至
   $n=2$所產生的光譜。
3. 帕申系列(紅外光區):電子由
   $n>3$降至
   $n=3$所產生的光譜。

這3個系列以外的都是紅外區，也就是降至

$n>3$的都是紅外光區

$\mathrm{各}\mathrm{系}\mathrm{列}\mathrm{譜}\mathrm{線}，\mathrm{以}\mathrm{能}\mathrm{量}\mathrm{最}\mathrm{低}\mathrm{之}\mathrm{譜}\mathrm{線}\mathrm{為}\mathrm{第}\mathrm{一}\mathrm{條}\mathrm{譜}\mathrm{線}，\mathrm{能}\mathrm{量}\mathrm{最}\mathrm{高}\mathrm{之}\mathrm{譜}\mathrm{為}\mathrm{最}\mathrm{末}\mathrm{一}\mathrm{條}(n=\mathrm{\infty }\to n=\mathrm{第}n\mathrm{條})$

---

原子軌域

原子軌域

• 波耳氫原子模型的缺點:
  1. 波耳的模型只能解釋單一電子所組成之原子或離子的光譜，例如:
     $H、H{e}^{+}、L{i}^{2+}$，對多電子之原子光譜不能解釋。
  2. 波耳的模型中，原子內的電子沿一定軌道在原子核的周圍作圓周運動，實際上電子並不是在核外循一定軌道做圓周運動。

---

• 量子力學的原子模型:科學家認為電子是在原子核附近的空間快速移動，電子的運動軌跡無法被預測，亦即無法知道電子下一瞬間會出現在何處。但能預測電子在空間中某個點的出現機率。

  1. 軌域:在原子核附近，電子出現機率較大之區域稱為軌域，化學家通常將含有電子雲
     $90\mathrm{\%}$機率之區域稱為原子之軌域。
  2. 軌域與量子數:

     1. 主量子數

        $(n)$ :
        1. 主量子數用來描述軌域及能量的大小。
        2. 主量子數
           $n=1、2、3、......$代表電子主殼層，依序以英文符號
           $K、L、M、N..$表示。

        $n$值愈大，軌域的範圍愈大，能量愈高。

     2. 角動量量子數

        $(\ell )$ :
        1. 角動量量子數是描述軌域的形狀。
        2. 對每一個
           $n$值而言都，可以有
           $n$個
           $\ell$值，即
           $\ell =0、1、2、3、...、(n-1)$，角動量量子數
           $\ell =0、1、2、3、...、(n-1)$代表電子副殼層，依序以
           $s、p、d、f、...$表示

        角動量量子數 $(\ell )$	0	1	2	3	4
        軌域名稱	s	p	d	f	g
        形狀	球形	啞鈴型	雙啞鈴型	-	-

        $n=3$時，

        $\ell$值有

        $0、1、2$，其意義為第

        $3$殼層中含

        $s$軌域、

        $p$軌域、

        $d$軌域，即有

        $3d、3p、3d$三種副殼層軌域

     3. 磁量子數

        $(m_{\ell })$ :
        1. 磁量子數描述軌域分布的方位及軌域數目。
        2. 對於每個
           $\ell$而言，可以有
           $(2\ell +1)\mathrm{個}{m}_{\ell }$值，即
           $m_{\ell }=+\ell 、...、0、...、-\ell$，意即每個角動量量子數
           $\ell$有
           $(2\ell +1)$個不同分布方位的軌域。

        $s\mathrm{軌}\mathrm{域}(\ell =0)$ 有1個

        $m_{\ell }$，代表

        $s\mathrm{軌}\mathrm{域}$僅有1種分布方向，也就是

        $s\mathrm{軌}\mathrm{域}$只有一個。依此類推:

        $p\mathrm{軌}\mathrm{域}\mathrm{有}3\mathrm{個}、d\mathrm{軌}\mathrm{域}\mathrm{有}5\mathrm{個}、f\mathrm{軌}\mathrm{域}\mathrm{有}7\mathrm{個}$

     4. 自旋量子數

        $(m_s)$ : 決定電子自轉方向。
        
        $\because m_s=+\frac{1}{2}{}_{\vee }-\frac{1}{2}。$
        
        $\therefore \mathrm{每}\mathrm{個}\mathrm{軌}\mathrm{域}\mathrm{可}\mathrm{容}\mathrm{納}\ast \ast 2\mathrm{個}\mathrm{不}\mathrm{同}\mathrm{自}\mathrm{轉}\mathrm{方}\mathrm{向}\mathrm{電}\mathrm{子}\ast \ast$
        
        $$\begin{array}{|lcccccccccc|}\hline \text{主殼層 }(n)& 1& & 2& & & 3& & & & 4\\ \text{副殼層 }(\ell )& 1s& 2s& 2p& 3s& 3p& 3d& 4s& 4p& 4d& 4f\\ \text{副殼層軌域數}& 1& 1& 3& 1& 3& 5& 1& 3& 5& 7\\ \text{主殼層軌域總數 }(n^2)& 1& & 4& & & 9& & & & 16\\ \text{最大電子容量 }(2n^2)& 2& & 8& & & 18& & & & 32\\ \hline\end{array}$$

     因為hackMD沒有完整支援

     $LATEX$所以不能用

     $table$環境，只能用

     $array$這簡陋的環境，他甚至不能合併儲存格我只能靠強制對齊

• 原子軌域形狀:

  1. $s\mathrm{軌}\mathrm{域}$ :在每一個
     $n\ge 1$的主層中，均有1個
     $s\mathrm{軌}\mathrm{域}$。
     1. $s\mathrm{軌}\mathrm{域}$形狀為球形。
     2. $n$越大，
        $ns\mathrm{軌}\mathrm{域}$的電子雲分布半徑越大，能量越大，即能階
        $1s<2s<3s$。
     3. 同個半徑的球面，電子出現的機率是一樣的，和方向無關。
  2. $p\mathrm{軌}\mathrm{域}$ :在每一個
     $n\ge 2$的主層中，均有3個
     $p\mathrm{軌}\mathrm{域}$。
     1. $p\mathrm{軌}\mathrm{域}$的電子雲分布在
        $x、y、z$三個互相垂直的軸，形狀是啞鈴形，依次稱為
        $p_x、p_y、p_z$軌域。
     2. 同一個主層的3個
        $p$軌域能量均相等，即能階
        $n{p}_x=n{p}_y=n{p}_z$。
     3. $p$軌域有方向性，例如不會在
        $x$平面以外發現
        $p_x$軌域電子。
  3. $d\mathrm{軌}\mathrm{域}$ :在每一個
     $n\ge 3$的主層中，均有5個
     $d\mathrm{軌}\mathrm{域}$。
     1. $d$軌域有方向性。
     2. $d\mathrm{軌}\mathrm{域}$形狀為雙啞鈴形。

---

原子能階

• 單電子之氫原子或類氫離子
  $(\mathrm{就}\mathrm{是}\mathrm{變}\mathrm{成}\mathrm{只}\mathrm{有}1\mathrm{個}\mathrm{電}\mathrm{子}，\mathrm{例}\mathrm{如}:H{e}^{+}、L{i}^{2+}):$
  1. 軌域能階高低由
     $n$值決定的，
     $n$越大，能階越大。
  2. 同一主層的
     $(n)$的
     $n$種副層軌域能階是一樣的。
     $$1s<2s=2p<3s=3s=3p=3d<4s=4p=4d=4f<...$$
• 多電子原子能階:
  1. 軌域能階由
     $n+\ell$值決定。
     1. $n+\ell$越大，能階越高。
     2. $n+\ell$相同時，則由
        $n$決定。
        $$1s<2s<2p<3s<3p<4s<3d<4p<5s...$$

假如是多電子原子同一主量子數

$n$的

$n^2$個軌域的能量不一定一樣。

---

1-3

電子組態

• 電子組態
  1. 原子中各電子在軌域的排列方式就是電子組態，會用以下方式表示:
     $$\mathrm{主}\mathrm{量}\mathrm{子}\mathrm{數}(n)\mathrm{角}\mathrm{動}\mathrm{量}\mathrm{量}\mathrm{子}\mathrm{數}(\ell {)}^{\mathrm{電}\mathrm{子}\mathrm{數}}\mathrm{例}\mathrm{如}:1s^2、3d^4$$
  2. 電子填充軌域的三大規則:
     1. 遞建原理:電子進入軌域後，要先從低能階的軌域進入，等低能階軌域都填滿後才可以進入高能階。
     2. 洪德定則:多個電子要進入同能階的同型軌域(如
        $p_x、p_y、p_z$)時，電子先以相同的自轉方向分別進入不同方向的軌域而不成對，等到每個軌域都有1個電子後，才讓自轉方向相反的電子進入以成對。

     以上兩個違反稱為激發態，都遵守則稱為基態，
     而以下這個假如違反就直接是不存在的

     3. 包立不相容原理:每個軌域只能容納最多2個電子，並且自轉方向必定相反。
  3. 電子組態表示的方法:
     1. 依據主層數的順序排，同一主層用
        $s、p、d、f$來排，再將各軌域的電子數寫在
        ${}^{\mathrm{右}\mathrm{上}\mathrm{角}}$
     2. 多電子原子若依照電子填充軌域的規則填入，所排序的方式，能量最低，被稱為基態電子組態，一般所謂的原子電子組態就是指這個。
     3. 原子序較大時，為了簡化紀錄，內層的電子組態會以前一周期的鈍氣的元素符號被
        $[]$包著的方式表示。
     4. 過渡元素依照能量由低至高填入，但電子組態按照
        $n$的大小來寫。
     5. 原子序
        $24、29$的鉻
        ${(}_{24}Cr)、\mathrm{銅}{(}_{29}Cu)$的
        $d\mathrm{軌}\mathrm{域}$分別是全半填滿
        $(3d^5)$和全填滿
        $(3d^{10})$，也就是原本理論上
        ${}_{24}Cr\mathrm{的}\mathrm{電}\mathrm{子}\mathrm{組}\mathrm{態}\mathrm{應}\mathrm{該}\mathrm{是}[Ar]3d^{4}4s^2{、}_{29}Cu\mathrm{要}\mathrm{是}[Ar]3d^{9}4s^2，$
        
        $\mathrm{但}\mathrm{實}\mathrm{際}{\mathrm{上}}_{24}Cr\mathrm{是}[Ar]3d^{5}4s^1{、}_{29}Cu\mathrm{是}[Ar]3d^{10}4s^1$

---

週期表

• 每1周期的第1個元素都是由1個新主層開始，也就是第
  $n$週期第1個元素是從
  $[\mathrm{前}\mathrm{一}\mathrm{個}\mathrm{鈍}\mathrm{氣}\mathrm{元}\mathrm{素}]ns$開始。
• 元素分類:
  1. 主族元素
     $(A\mathrm{族}\mathrm{元}\mathrm{素})$:最後1個電子填入
     $s\mathrm{或}p\mathrm{軌}\mathrm{域}$的元素。
     1. 位置:在週期表
        $\mathrm{I}\mathrm{A}\sim \mathrm{V}\mathrm{I}\mathrm{I}\mathrm{I}\mathrm{A}$族，包含了金屬與非金屬元素。
     2. 價軌域:
        $ns\mathrm{與}np$，除了
        $He$以外的價電子數都是和族數一樣。

        族數	$\mathrm{I}\mathrm{A}$	$\mathrm{I}\mathrm{I}\mathrm{A}$	$\mathrm{I}\mathrm{I}\mathrm{I}\mathrm{A}$	$\mathrm{I}\mathrm{V}\mathrm{A}$	$\mathrm{V}\mathrm{A}$	$\mathrm{V}\mathrm{I}\mathrm{A}$	$\mathrm{V}\mathrm{I}\mathrm{I}\mathrm{A}$	$\mathrm{V}\mathrm{I}\mathrm{I}\mathrm{I}\mathrm{A}$
        價電子組態	$n{s}^1$	$n{s}^2$	$n{s}^{2}n{p}^1$	$n{s}^{2}n{p}^2$	$n{s}^{2}n{p}^3$	$n{s}^{2}n{p}^4$	$n{s}^{2}n{p}^5$	$n{s}^{2}n{p}^6$
        價電子數	1	2	3	4	5	6	7	8

        價電子就是原子最外層的電子，因為最容易失去或和其他原子共用，故價電子可以決定該原子的化學性質，價電子所在的軌域稱為價軌域(價電子組態)。

     3. 鈍氣元素:位於週期表最右端，屬於
        $\mathrm{V}\mathrm{I}\mathrm{I}\mathrm{I}\mathrm{A}$族元素，除了
        $He\mathrm{為}1s^2$以外其餘價電子型態皆為
        $n{s}^{2}n{p}^6$，無色無味，非常不活潑。
  2. 過渡元素
     $(B\mathrm{族}\mathrm{元}\mathrm{素})$:最後1個電子填入
     $d\mathrm{軌}\mathrm{域}$的元素。
     1. 位於週期表中間的$B%族，全都是金屬。
     2. 價軌域:
        $ns、(n-1)d$。
  3. 內過渡元素:最後1個電子填入
     $f\mathrm{軌}\mathrm{域}$的元素。
     • 位於週期表下面兩排。
     1. 鑭系:第6週期，最後的電子填
        $4f$。
     2. 錒系:第7週期，最後的電子填
        $5f$。
     3. 價軌域:
        $ns、(n-1)d、(n-2)f$。

---

原子性質的週期性

原子半徑與離子半徑:

• 同族元素越下面半徑越大
  $$\because \mathrm{主}\mathrm{量}\mathrm{子}\mathrm{數}\mathrm{越}\mathrm{大}，\mathrm{電}\mathrm{子}\mathrm{離}\mathrm{核}\mathrm{越}\mathrm{遠}，\mathrm{半}\mathrm{徑}\mathrm{越}\mathrm{大}$$
• 同週期越左半徑越大
  $$\because \mathrm{主}\mathrm{量}\mathrm{子}\mathrm{數}\mathrm{一}\mathrm{樣}，\mathrm{核}\mathrm{電}\mathrm{荷}\mathrm{越}\mathrm{大}，\mathrm{核}\mathrm{對}\mathrm{電}\mathrm{子}\mathrm{吸}\mathrm{引}\mathrm{力}\mathrm{越}\mathrm{大}，\mathrm{半}\mathrm{徑}\mathrm{越}\mathrm{小}$$
• 同電子，原子序最小的，原子或離子的半徑最大
  $$\because \mathrm{原}\mathrm{子}\mathrm{序}\mathrm{越}\mathrm{大}，\mathrm{核}\mathrm{對}\mathrm{電}\mathrm{子}\mathrm{吸}\mathrm{引}\mathrm{力}\mathrm{越}\mathrm{大}，\mathrm{半}\mathrm{徑}\mathrm{越}\mathrm{小}$$
• 相同核電荷，電子數越多，電子斥力愈大，半徑越大。

---

游離能

• 將氣態原子最外層電子抓走，需要的能量就稱為游離能
  $(\mathrm{I}\mathrm{E})$。
• 元素之連續游離能:
  $\mathrm{I}{\mathrm{E}}_{\mathrm{n}}\mathrm{就}\mathrm{是}\mathrm{移}\mathrm{除}\mathrm{第}\mathrm{n}\mathrm{個}\mathrm{電}\mathrm{子}\mathrm{需}\mathrm{要}\mathrm{的}\mathrm{能}\mathrm{量}$。
  
  $$M(g)\to M^{+}(g)+e^{-}\mathrm{\Delta }H=\mathrm{游}\mathrm{離}\mathrm{能}>0$$
• 同一個原子中當遇到突然變大
  $(\mathrm{I}{\mathrm{E}}_{\mathrm{n}-1}\gg \mathrm{I}{\mathrm{E}}_{\mathrm{n}})$，代表此原子有
  $n$個價電子。
• 影響游離能大小:
  1. 原子半徑越大，游離能越小。
  2. 核電荷越大，游離能越大。
  3. 電子組態越穩定，游離能越大。
• 游離能的周期性:
  1. 同族中越下面周期越小。
  2. 同週期元素往右呈鋸齒狀增加。
  3. 同電子數，原子序越小，游離能越大
  4. 陰離子的游離能比中性原子和陽離子小。
  5. 鹵素游離能:
     $C{l}^{-}>F^{-}>B^{-}>I^{-}$。

---

電子親和力

• 從一個帶負電的氣態陰離子抓走1個電子的能量變化就是電子親和力
  
  $$X^{-}(g)\to X(g)+e^{-}\mathrm{\Delta }H=X\mathrm{元}\mathrm{素}\mathrm{的}\mathrm{電}\mathrm{子}\mathrm{親}\mathrm{和}\mathrm{力}$$
  
  $\mathrm{\Delta }H\mathrm{越}\mathrm{大}\mathrm{代}\mathrm{表}\mathrm{該}\mathrm{原}\mathrm{子}\mathrm{越}\mathrm{能}\mathrm{接}\mathrm{受}\mathrm{電}\mathrm{子}，\mathrm{也}\mathrm{越}\mathrm{能}\mathrm{吸}\mathrm{引}\mathrm{電}\mathrm{子}，\mathrm{放}\mathrm{熱}\mathrm{較}\mathrm{多}$
• 核電荷越小、原子半徑越大、中性原子組態越穩定，氣態原子越不接受並吸引電子，也就是電子親和力較小。
• 非金屬電子親和力通常大於金屬。
• $\mathrm{I}\mathrm{I}\mathrm{A}、\mathrm{V}\mathrm{I}\mathrm{I}\mathrm{I}\mathrm{A}、\mathrm{N}$的電子親和力為負，
  $\mathrm{V}\mathrm{A}$較小但為正。
• 同週期中
  $\mathrm{V}\mathrm{I}\mathrm{I}\mathrm{A}$電子親和力最大。
• 鹵素的電子親和力:
  $Cl>F>Br>I$。
• 中性原子的電子親和力小於游離能。

---

重點整理

$$\begin{array}{rl}& c=\lambda \nu =3\times {10}^8,m/s\\ & R_H=1.097\times {10}^{-2},n{m}^{-1}\\ & E_n=-\frac{k}{n^2}\\ & E=h\nu =\frac{hc}{\lambda }\propto \nu \propto \frac{1}{\lambda }=R_H(\frac{1}{n_L{}^2}-\frac{1}{n_H{}^2})\propto (\frac{1}{n_L{}^2}-\frac{1}{n_H{}^2})\\ & \mathrm{\Delta }E=h\mathrm{\Delta }\nu =k(\frac{1}{n_L{}^2}-\frac{1}{n_H{}^2})\end{array}$$

系列	終點 $n$	區域
來曼	1	紫外光
巴耳末	2	可見光
帕申	3	紅外光

$\mathrm{原}\mathrm{子}\mathrm{半}\mathrm{徑}\downarrow ;\Rightarrow ;\mathrm{游}\mathrm{離}\mathrm{能}\uparrow$

$\mathrm{核}\mathrm{電}\mathrm{荷}\uparrow ;\Rightarrow ;\mathrm{原}\mathrm{子}\mathrm{半}\mathrm{徑}\downarrow ;\Rightarrow ;\mathrm{游}\mathrm{離}\mathrm{能}\uparrow$

同族（由上到下）

• $\mathrm{層}\mathrm{數}\mathrm{增}\mathrm{加}(n\uparrow )$
• 半徑變大
• 游離能變小

$Li<Na<K（\mathrm{半}\mathrm{徑}）$

$Li>Na>K（\mathrm{游}\mathrm{離}\mathrm{能}）$

同週期（由左到右）

• 核電荷增加
• 有效核電荷增加
• 半徑變小
• 游離能變大

例：

$Na>Mg>Al（\mathrm{半}\mathrm{徑}）$

$Na<Mg<Al（\mathrm{游}\mathrm{離}\mathrm{能}）$

---

等電子（電子數相同）

• 核電荷越大 → 吸引越強 → 半徑越小

例：

$N^{3-}>O^{2-}>F^{-}>N{a}^{+}>M{g}^{2+}$

$\mathrm{原}\mathrm{子}\mathrm{序}\uparrow \Rightarrow \mathrm{半}\mathrm{徑}\downarrow$$

---

同元素（不同離子）

• 電子越多 → 排斥越大 → 半徑越大

例：

$O^{2-}>O>O^{+}$

---

游離能

基本：

$\mathrm{半}\mathrm{徑}\mathrm{小}\Rightarrow \mathrm{游}\mathrm{離}\mathrm{能}\mathrm{大}$

---

趨勢：

$ 同族：↓$
$ 同週期：↑（整體）$

---

第二週期第一游離能

$Ne>F>O>N>C>Be>B>Li$

• $(N>O)（\mathrm{半}\mathrm{滿}\mathrm{穩}\mathrm{定}）$
• $(Be>B)（s\mathrm{軌}\mathrm{域}>p\mathrm{軌}\mathrm{域}）$

---

「半徑小＝抓得緊＝游離能大；核電荷大＝抓更緊」

---

數學公式

$\mathrm{△}ABC\mathrm{有}\mathrm{三}\mathrm{個}\mathrm{邊}a、b、c$

$$\begin{array}{rl}& \tan \theta =\frac{\sin \theta }{\cos \theta }\\ & {\cos }^2\theta +{\sin }^2\theta =1\\ & 1+{\tan }^2\theta =\frac{1}{{\cos }^2\theta }\end{array}$$

$\frac{a}{\sin A}=\frac{b}{\sin B}=\frac{c}{\sin C}=2R$

$$\begin{array}{rl}& a^2=b^2+c^2-2bc\cos A\\ & b^2=c^2+a^2-2ca\cos A\\ & c^2=a^2+b^2-2ab\cos C\end{array}$$

$$\begin{array}{rl}& s\mathrm{為}\mathrm{弧}\mathrm{長}r\mathrm{為}\mathrm{半}\mathrm{徑}\\ & s=2r\pi \times \frac{a^{\circ }}{{360}^{\circ }}=r\times \frac{a^{\circ }}{{180}^{\circ }}\pi =r\theta \\ & \theta =\frac{a^{\circ }}{{180}^{\circ }}\pi =\frac{s}{r}\\ & 1\mathrm{弧}\mathrm{度}(rad)=\frac{{180}^{\circ }}{\pi }\approx {57.3}^{\circ }\\ & \pi \mathrm{弧}={180}^{\circ }\\ & \end{array}$$

$$\begin{array}{rl}& \mathrm{負}\mathrm{角}\mathrm{公}\mathrm{式}\\ & \cos (-\theta )=cos\theta \\ & \sin (-\theta )=-\sin \theta \\ & \mathrm{餘}\mathrm{角}\mathrm{公}\mathrm{式}\\ & \cos (\frac{\pi }{2}-\theta )=\sin \theta \\ & \sin (\frac{\pi }{2}-\theta )=\cos \theta \\ & \mathrm{加}\mathrm{法}\mathrm{定}\mathrm{理}\\ & \cos (\alpha +\beta )=cos\alpha \cos \beta -\sin \alpha \sin \beta \\ & cos(\alpha -\beta )=\cos \alpha \cos \beta +\sin \alpha \sin \beta \\ & \sin (\alpha +\beta )=\sin \alpha \cos \beta +\cos \alpha \sin \beta \\ & \sin (\alpha -\beta )=\sin \alpha \cos \beta -\cos \alpha \sin \beta \\ & \tan (\alpha +\beta )=\frac{\tan \alpha +\tan \beta }{1-\tan \alpha \tan \beta }\\ & \tan (\alpha -\beta )=\frac{\tan \alpha -\tan \beta }{1+\tan \alpha \tan \beta }\\ & \mathrm{二}\mathrm{倍}\mathrm{角}\mathrm{公}\mathrm{式}\\ & \cos 2\alpha ={\cos }^2\alpha -{\sin }^2\alpha \\ & \sin 2\alpha =2\sin \alpha \cos \alpha \\ & \tan 2\alpha =\frac{2\tan \alpha }{1-{\tan }^2\alpha }\\ & \mathrm{半}\mathrm{角}\mathrm{公}\mathrm{式}\\ & \cos \frac{\theta }{2}=\sqrt{\frac{1+\cos \theta }{2}}\\ & \sin \frac{\theta }{2}=\sqrt{\frac{1-\cos \theta }{2}}\\ & \tan \frac{\theta }{2}=\sqrt{\frac{1-\cos \theta }{1+\cos \theta }}\\ & \mathrm{三}\mathrm{角}\mathrm{函}\mathrm{數}\mathrm{疊}\mathrm{合}\\ & a\sin \theta +b\cos \theta =\sqrt{a^2+b^2}\sin (\theta +\alpha )\\ & \alpha \mathrm{是}\mathrm{通}\mathrm{過}\mathrm{半}\mathrm{徑}\mathrm{為}\sqrt{a^2+b^2}\mathrm{圓}\mathrm{上}\mathrm{一}\mathrm{點}(a,b)\mathrm{和}x\mathrm{軸}\mathrm{的}\mathrm{夾}\mathrm{角}，\mathrm{並}\mathrm{滿}\mathrm{足}\mathrm{以}\mathrm{下}2\mathrm{個}\\ & \cos \alpha =\frac{a}{\sqrt{a^2+b^2}}\sin \alpha =\frac{b}{\sqrt{a^2+b^2}}\\ & \end{array}$$

海龍公式推導

$$\begin{array}{rl}& \text{由餘弦定理：}\\ & \cos A=\frac{b^2+c^2-a^2}{2bc}\\ & \Rightarrow \sin A=\sqrt{1-{\cos }^{2}A}\\ & \text{面積公式：}\\ & S=\frac{1}{2}bc\sin A\\ & \Rightarrow S=\frac{1}{2}bc\sqrt{1-{\left(\frac{b^2+c^2-a^2}{2bc}\right)}^2}\\ & =\frac{1}{2}bc\sqrt{\frac{4b^2{c}^2-(b^2+c^2-a^2{)}^2}{4b^2{c}^2}}\\ & =\frac{1}{4}\sqrt{4b^2{c}^2-(b^2+c^2-a^2{)}^2}\\ & \text{整理後可得：}\\ & S=\frac{1}{4}\sqrt{(a+b+c)(-a+b+c)(a-b+c)(a+b-c)}\\ & \text{令半周長 }s=\frac{a+b+c}{2}\\ & \Rightarrow S=\sqrt{s(s-a)(s-b)(s-c)}\end{array}$$

三角函數表

$\sec \theta =\frac{1}{\cos \theta }$

$\csc \theta =\frac{1}{\sin \theta }$

$\cot \theta =\frac{1}{\tan \theta }$

$\theta$	弧度	$\sin \theta$	$\cos \theta$	$\tan \theta$	$\cot \theta$	$\sec \theta$	$\csc \theta$
$0^{\circ }$	$0$	$0$	$1$	$0$	—	$1$	—
${15}^{\circ }$	$\frac{\pi }{12}$	$\frac{\sqrt{6}-\sqrt{2}}{4}$	$\frac{\sqrt{6}+\sqrt{2}}{4}$	$2-\sqrt{3}$	$2+\sqrt{3}$	$\sqrt{6}-\sqrt{2}$	$\sqrt{6}+\sqrt{2}$
${30}^{\circ }$	$\frac{\pi }{6}$	$\frac{1}{2}$	$\frac{\sqrt{3}}{2}$	$\frac{1}{\sqrt{3}}$	$\sqrt{3}$	$\frac{2}{\sqrt{3}}$	$2$
${45}^{\circ }$	$\frac{\pi }{4}$	$\frac{\sqrt{2}}{2}$	$\frac{\sqrt{2}}{2}$	$1$	$1$	$\sqrt{2}$	$\sqrt{2}$
${60}^{\circ }$	$\frac{\pi }{3}$	$\frac{\sqrt{3}}{2}$	$\frac{1}{2}$	$\sqrt{3}$	$\frac{1}{\sqrt{3}}$	$2$	$\frac{2}{\sqrt{3}}$
${75}^{\circ }$	$\frac{5\pi }{12}$	$\frac{\sqrt{6}+\sqrt{2}}{4}$	$\frac{\sqrt{6}-\sqrt{2}}{4}$	$2+\sqrt{3}$	$2-\sqrt{3}$	$\sqrt{6}+\sqrt{2}$	$\sqrt{6}-\sqrt{2}$
${90}^{\circ }$	$\frac{\pi }{2}$	$1$	$0$	—	$0$	—	$1$

---

物理

動量衝量

$\overrightarrow{p}=m\overrightarrow{v}=\sqrt{2mk}k=\frac{1}{2}m{v}^2=\frac{p^2}{2m}$

$\text{if}m\mathrm{相}\mathrm{同}:\mathrm{\Delta }\overrightarrow{p}=m\mathrm{\Delta }\overrightarrow{v}$

$\mathrm{\Delta }\overrightarrow{p}=\overrightarrow{p}-\overrightarrow{p_0}=m\mathrm{\Delta }\overrightarrow{v}=m\overrightarrow{a}\mathrm{\Delta }t=\overrightarrow{F}\cdot \mathrm{\Delta }t=\overrightarrow{J}$

$\mathrm{\Delta }m=0:\overrightarrow{F_{av}}=\frac{\mathrm{\Delta }\overrightarrow{p}}{\mathrm{\Delta }t}=m\frac{\mathrm{\Delta }\overrightarrow{v}}{\mathrm{\Delta }t}=m\overrightarrow{a_{av}}$

$1\mathrm{質}\mathrm{點}\mathrm{系}\mathrm{統}\mathrm{中}\mathrm{有}{m}_1\mathrm{到}{m}_N，\mathrm{總}\mathrm{共}N\mathrm{個}\mathrm{點}$

$\mathrm{系}\mathrm{統}\mathrm{質}\mathrm{量}M=m_1+m_2+.....m_N$

$\mathrm{質}\mathrm{心}\mathrm{位}\mathrm{置}\overrightarrow{r_c}=\frac{m_1\overrightarrow{r_1}+m_2\overrightarrow{r_2}+....m_N\overrightarrow{r_N}}{m_1+m_2+.....m_N}$

$\mathrm{質}\mathrm{心}\mathrm{速}\mathrm{度}\overrightarrow{v_c}=\frac{m_1\overrightarrow{v_1}+m_2\overrightarrow{v_2}+....m_N\overrightarrow{v_N}}{m_1+m_2+.....m_N}$

$\mathrm{質}\mathrm{心}\mathrm{加}\mathrm{速}\mathrm{度}\overrightarrow{a_c}=\frac{m_1\overrightarrow{a_1}+m_2\overrightarrow{a_2}+....m_N\overrightarrow{a_N}}{m_1+m_2+.....m_N}$

$\overrightarrow{P_{center}}=\overrightarrow{P_{total}}=\mathrm{所}\mathrm{有}\mathrm{質}\mathrm{點}\mathrm{之}\mathrm{動}\mathrm{量}\mathrm{向}\mathrm{量}\mathrm{和}$
當系統不受外力作用或淨力為零時時，動量不會改變，稱為動量守恆。

力矩

$\overrightarrow{\tau }\mathrm{是}\mathrm{力}\mathrm{矩}\overrightarrow{r}\mathrm{是}\mathrm{支}\mathrm{點}\mathrm{到}\mathrm{受}\mathrm{力}\mathrm{點}\mathrm{的}\mathrm{向}\mathrm{量}\overrightarrow{L}\mathrm{是}\mathrm{角}\mathrm{動}\mathrm{量}$

$\tau =\overrightarrow{r}\times \overrightarrow{F}=r(F\sin \theta )=F\cdot b=r{F}_{\perp }$

$\overrightarrow{\tau }=\overrightarrow{r}\times \overrightarrow{F}=\overrightarrow{r}\times \frac{d\overrightarrow{P}}{dt}=\frac{d(\overrightarrow{r}\times \overrightarrow{P})}{dt}-\frac{d\overrightarrow{r}}{dt}\times \overrightarrow{P}=\frac{d(\overrightarrow{r}\times \overrightarrow{P})}{dt}=\underset{\mathrm{\Delta }t\to 0}{lim}\frac{\mathrm{\Delta }\overrightarrow{L}}{\mathrm{\Delta }t}\mathrm{所}\mathrm{以}\mathrm{說}\mathrm{力}\mathrm{矩}\mathrm{就}\mathrm{是}\mathrm{角}\mathrm{動}\mathrm{量}\mathrm{的}\mathrm{時}\mathrm{變}\mathrm{率}，\mathrm{就}\mathrm{像}\mathrm{是}\overrightarrow{F}=\frac{d\overrightarrow{P}}{dt}$

$\overrightarrow{L}=\overrightarrow{r}\times \overrightarrow{p}=\overrightarrow{r}\times (m\overrightarrow{v})$

$\overrightarrow{\tau }=\overrightarrow{r}\times \overrightarrow{F}=\frac{\mathrm{\Delta }\overrightarrow{L}}{\mathrm{\Delta }t}\mathrm{當}\mathrm{受}\mathrm{到}\mathrm{的}\mathrm{力}\mathrm{矩}\mathrm{為}0\mathrm{時}，\mathrm{角}\mathrm{動}\mathrm{量}\mathrm{不}\mathrm{會}\mathrm{隨}\mathrm{著}\mathrm{時}\mathrm{間}\mathrm{改}\mathrm{變}，\mathrm{稱}\mathrm{為}\mathrm{角}\mathrm{動}\mathrm{量}\mathrm{守}\mathrm{恆}$

---

英文

課文

7

Paragraph 1
Everyone has his or her own favorite way of spending free time. Some like to have fun by
playing video games or surfing social networking sites. Others choose to keep their minds sharp by reading books and newspapers. Still others, however, seek fun as well as knowledge. Such people are the perfect audience for the series of short online videos known as TED Talks, which share information from expert speakers on various topics.
每個人都有自己打發空閒時間的最愛方式。有些人喜歡藉著打電動遊戲或是瀏覽社交網站
來尋找樂趣。有些人選擇藉著閱讀書籍報紙來讓思維敏捷。然而，還有些人尋求樂趣與知識
。這類人正是一系列稱為TED演講的網路短片的理想觀眾，這些短片分享由各領域專家演講
者所提供的資訊。
Paragraph 2
The history behind TED, which stands for Technology, Entertainment, Design, is also worth talking about. Ever since this nonprofit foundation was established in 1984, it has provided a platform for people to share their thoughts and findings. The first conference was held that same year, with the slogan “ideas worth spreading.” During the meeting, each speaker was given eighteen minutes to present his or her ideas. As TED conferences became increasingly popular, it was clear to the organizers that they should invite thinkers from a broader range of fields to come and speak. These fields included philosophy, business, and medicine. In 2007, the website TED.com was launched, and many of the speakers’ talks were uploaded for the public to watch for free. At present, the collection of TED Talk videos is growing week by week, and it has helped spread new ideas around the world.
TED代表科技、娛樂與設計，其背後的歷史也值得一提。自1984年創立起，這個非營利組
織一直提供一個讓人們分享想法與調查結果的機會。首場研討會在同年舉辦，以「值得傳播
的想法」為口號。在該場會議中，每位講者有十八分鐘可以呈現自己的想法。隨著TED研討
會愈來愈受到歡迎，對籌辦者而言，顯然他們應該自較廣泛的領域種類邀請思想家蒞臨演講
。這些領域包括哲學、商業以及醫學。在2007年，網站TED.com發布，許多講者的演講都被
上傳，讓大眾可以免費觀看。目前TED演講的影片總量每週都在增加，並幫助將新觀念傳播
至世界各地。

Paragraph 3
Over the years, numerous celebrities have given TED Talks and shared valuable insights with
their audiences. One was chef Jamie Oliver, who presented his idea of starting a food revolution.
Oliver wanted to improve people’s health by teaching everyone how to choose and prepare healthy
meals. Another was James Cameron, the director of the movies Aliens and Avatar. Cameron talked
about his childhood fascination with science fiction. He also spoke of how his interest in space,aliens, and robots eventually led him to make blockbuster films. Still another was Bill Gates, the co-founder of Microsoft. It is interesting that Bill Gates didn’t talk about computers. Instead, he discussed the importance and the methods of controlling the spread of diseases like Ebola. These are just a few examples of the celebrity speakers who have left millions feeling inspired through their TED Talks.
這些年來，許多名人做了TED 演講，並與他們的觀眾分享了寶貴的見解。其中一位是主
廚傑米．奧利佛，他介紹了他發起食物革命的理念。奧利佛想要藉由教導每個人如何選擇及
準備健康的餐點，來改善人們的健康。另一位講者是詹姆斯．卡麥隆，電影《異形2》及《
阿凡達》的導演。卡麥隆談到他童年時對科幻小說的著迷。他也說到他對太空、外星人以及

機器人的興趣，最終引導他拍出賣座電影。還有另一位講者是微軟的共同創辦人比爾．蓋茲
。有趣的是比爾．蓋茲並沒有談論電腦。相反地，他探討了控制像伊波拉等疾病蔓延的重要
性與方法。這些只是一些名人演講者透過他們的TED演講讓數百萬人受到啟發的例子。
Paragraph 4
Listening to one of these TED Talks is like standing on the shoulders of a giant—you get to see
farther and understand more. You won’t realize just how much you can learn in eighteen minutes
unless you give it a try. In fact, there is a good chance that these talks will broaden your horizons and even inspire you to try to change the world.
聽這些TED 演講之中的一場就像站在一位巨人的肩膀上──你能夠看得更遠，懂得更多。
除非你嘗試聽一次，否則你不會明白你在十八分鐘內可以學到多少東西。事實上，很有可能
這些演講將會拓展你的視野，甚至啟發你去設法改變這個世界。

---

8

Paragraph 1
Taking part in a student exchange program has really opened my eyes to the cultural
differences between my country and Taiwan. One of the most memorable parts of my trip occurred
when my host family invited me to a wedding banquet in Kaohsiung.
參加交換學生計畫真的讓我對於我的國家和臺灣之間的文化差異大開眼界。旅程中最令人
難忘的部分之一發生在我的接待家庭邀請我到高雄參加的一場婚宴之時。

Paragraph 2
Upon arriving at the banquet, I soon realized that it was totally different from what I’d expected. Back in the US, banquets are usually held in large dining halls. This one, on the other hand, was taking place right out in the street! Put up to shelter all the guests from the fierce sun, a huge tent occupied nearly half the street. However, the pedestrians or the people in passing vehicles paid no attention. Under the tent, guests sat at large round tables, chatting cheerfully. At one end of this temporary tent, there were cooks and assistants working energetically to prepare platters of delicious-looking food.
一到宴席會場，我很快就發現跟我預期的完全不同。在美國家鄉，宴席通常辦在大宴會廳
。然而，這一場宴席卻辦在外頭的馬路上！一個大帳篷被搭了起來為所有的婚禮賓客遮蔽烈
日，也就占據了幾乎一半的馬路。然而，路人或是來往車輛上的人都不予理會。在帳篷下，
賓客們坐於大圓桌，開懷閒聊。在這個臨時帳篷的一端，有廚師和助手正奮力地工作，準備
一盤盤看起來很美味的食物。

Paragraph 3
Being quite curious about how this fascinating custom of “open-air” banquets had come about, I
asked my host parents. The host father explained that this kind of banquet, known as a “ban-doh” in
Taiwanese, originated in the countryside. In the old days, when people gathered for a special event
such as a wedding or an elder’s birthday, everyone in the neighborhood would cooperate to arrange a ban-doh. The host would prepare all the ingredients for the meal, and the neighbors would help
out. Some would do the cooking, while others might provide tables, chairs, and eating utensils or
assist in other ways. They would then all relax and enjoy the banquet together. The ban-doh back
then was all about enjoying a sense of community and togetherness.
我相當好奇這個迷人的「露天」宴席習俗如何發生，我問了接待家庭的父母。接待家庭的
爸爸解釋說，這種臺語稱做「辦桌」的宴席起源於鄉間。在過去，當人們為了特別的事情（
如婚禮或長輩的生日）相聚時，附近的每個人就會合作安排一場辦桌。主人會準備這餐所有
的食材，鄰居們都會來幫忙。有些人負責煮菜，另一些人則負責提供桌椅及餐具或以其他方
式幫忙。然後，他們就會放鬆，一起享受這場宴席。那時候的辦桌主要是享受社群歸屬及團
聚的感覺。
Paragraph 4
My host mother added that toward the end of the banquet, the host would provide containers for
the guests to pack up the leftovers and take them home. Since it was usually late and dark when the
guests started leaving, the host would also often hand out torches to them to help light their way
home. Seeing lines of people strolling home with torches and bags of food in their hands is
something that older folks in Taiwan still remember. Although some aspects of the ban-doh have
changed in modern times, the spirit of gathering together to have fun has always remained.

我的接待家庭媽媽補充說，接近宴席的尾聲，主人會提供容器給賓客們打包剩菜並帶回家
。因為賓客們開始離開時通常時間已晚、天色又暗，主人也經常會發放火把給他們，以幫忙
點亮他們回家的路。看著一排排的人手裡拿著火把和打包的食物散步回家，是老一輩臺灣人
仍記得的光景。雖然辦桌的一些作法在現代已經改變，歡聚一堂的精神一直維持不變。
Paragraph 5
　　Having the chance to experience this fascinating event, I feel truly lucky. It is the first story that
I will share with my friends and family when they ask me about my student exchange experience in
Taiwan.
能有機會體驗這個迷人的活動，我感到很幸運。當我的朋友家人問我關於在臺灣當交換學
生的經驗時，這是我頭一件會跟他們分享的事情。

---

9

Paragraph 1
Have you ever heard the term “paparazzi”? Or how about “Photoshop” used as a verb? Both of
these are examples of eponyms. An eponym is a word which usually started out as the name of
someone or something but took on a more general meaning later on.
你有沒有聽過「狗仔隊」？或是Photoshop當成動詞用呢？這兩個詞都是「借名成字」的
例子。所謂借名成字，一開始原為某人或某物的名字，之後卻被賦予了比較普遍的意義。
Paragraph 2
An example of an eponym that is** derived from** a person’s name is “paparazzi.” It is said that this
word came from a character called Paparazzo in the Italian film La Dolce Vita. Set in Rome, the
film is about the writer of a popular newspaper column featuring celebrity gossip. Paparazzo is a photographer who works with the writer to reveal the secret lives of celebrities. After the film was released in 1960, people began to use the word paparazzo and its plural form paparazzi to refer to all photographers who chase celebrities around.
由人物名稱借代而得的一個例子便是paparazzi（狗仔隊）。據說，此詞源自於義大利電影
《甜蜜的生活》中一位名為Paparazzo的角色。電影背景設定在羅馬，關於一位專寫名人八卦
的名專欄作家。劇中，Paparazzo是與這位作家搭檔的攝影記者，將名人的私密生活公諸於世
。影片於1960年上映後，人們便開始將paparazzo與其複數型paparazzi用來泛指到處跟拍名人
的狗仔隊。
Paragraph 3
Product-based eponyms such as Photoshop, on the other hand, are brand names that are
commonly used to describe other similar products, or in this case an action. Photoshop is an image-editing software program created by Adobe Inc. It is used to create, modify, or digitally combine images and photographs. Since it was first released in 1987, Photoshop has become the standard software used by photographers and designers around the world. It became so widely known that over time, people began to use “Photoshop” as a verb to mean “to edit a photo.” For example, no
matter what software program is actually used, you could say, “The picture has obviously been
photoshopped.” In the beginning, Adobe was not pleased that people were using their product name
to describe the work of other companies’ products, but the eponym has become too popular for
them to stop its widespread usage.
另一方面，如Photoshop等根據產品而生成的字，都是一些品牌名稱，一般用來描述與其
類似的產品，或是以Photoshop而言則是用來描述一個動作。Photoshop是一個由Adobe公司所
開發的影像處理軟體，用來繪製、修改或數位合成影像和照片。自1987年推出以來
，Photoshop便成為全球攝影師與設計師使用的標準軟體。由於這個軟體太廣為人知，時間
一久大家逐漸開始將Photoshop當成動詞來表達「編輯圖片」之意。舉例來說，不管你實際
上用了什麼影像編輯軟體，你都可以說：「這張圖很明顯被photoshop過了。」一開始
，Adobe對於自家產品名被人用來描述其他公司產品所做的事不太高興，但這樣的借代用法
變得太普遍，擋也擋不住。
Paragraph 4
　 As you can see, eponyms play an important role in creating new words in our society. Language is constantly changing with the adoption of new words and alternative uses for existing words. Who knows what new words we will think up next?

如你所見，借名成字在我們社會中扮演造新字的要角。隨著新字和舊字新用的情況產生，
語言也在不斷變化。誰會知道我們接下來又會想出什麼新字呢？

---

單字

7

1. seek [sik] vt. 尋求；尋找　(sought—sought—seeking) to look for, or pursue
   Jenny’s father is eager to make more money and is seeking new ways of growing his business.

2. audience [ɔdɪəns] n. [C] 觀眾；聽眾　a group of people who gather together to listen to a talk or watch a performance
   Though Johnny had never given a speech to an audience of over two thousand people, he wasn’t nervous at all when speaking on the stage.

3. series[siriz] n. [C] 系列　a group of similar events or creative works
   Harry Potter is a series of novels that is popular among readers around the world.

4. technology [tɛk nɑlədʒɪ] n. [U, C] 科技　useful ways in which scientific
   knowledge is applied
   The rapid development in medical technology can help save millions of patients’ lives.
   Our company is experimenting with new technologies in order to make better products.

• technological [ˏtɛknə lɑdʒɪkḷ] adj. 科技的
  Technological advances in storing energy have reduced the time needed to charge electric car batteries.

5. worth [wɝθ] adj. 值得……的　good enough for
   The restaurant serves excellent French cuisine. It’s worth a try.

• worth adj. 價值⋯⋯的
  The violin shown in the museum is worth six million dollars.
• worth [wɝθ] n. [U] 價值；意義
  Leonard proved his worth to his basketball team by scoring more than thirty points in the game.
• worthy [wɝðɪ] adj. 值得……的
  The scientific achievements of Einstein are worthy of our respect.

6. foundation [faʊn deʃən] n. [C] 基金會　an organization or operation
   established to provide money for a certain purpose
   Two years ago, Monica set up a foundation aimed at finding a cure for breast cancer.
   - foundation n. [C] 基礎
   This course provides a solid foundation in web design. It covers all the basic skills.
   found [faʊnd] vt. 創立；建設
   Google was founded in 1998 by two students at Stanford University.

7. conference [ kɑnfərəns] n. [C] 會議；研討會　a large formal meeting in which
   people gather to talk about important matters
   Clara is attending a conference with two co-workers in Los Angeles.

8. increasingly [ɪnkrisɪŋlɪ] adv. 愈來愈……　more and more
   As summer approaches, the days become increasingly warm.

• increase [ɪn kris] vt. vi. 增加
  Over the last twelve months, the bakery has increased the price of its banana bread by 15%.
  Our global population will continue to increase with time and is set to reach around ten billion by 2050.
• increase [ɪnkris] n. [C, U] 增加
  An increase in average temperatures is causing the snow in this region to melt earlier than usual.
  According to reports, the number of foreign tourists seeking to experience a taste of Taiwan seems to be on the increase.

9. organizer [ ɔrgəˏnaɪzɚ] n. [C] 組織者；籌辦者　a person who plans or
   arranges a certain event
   The main organizer of the parade is a woman who has been planning weddings and graduation ceremonies for years.

• organize [ɔrgəˏnaɪz] vt. 組織；籌辦　
  While organizing Jasmine’s surprise party, her friends managed to keep all the plans secret from her.
• organization [ˏɔrgənə zeʃən] n. [C] 組織；機構
  Danny is the leader of an international organization that helps children with rare diseases.

10. broad [brɔd] adj. 廣泛的　covering a wide variety
    Our school provides numerous courses and a broad choice of club activities for students.

• broad adj. 寬闊的
  We walked down a broad street lined with trees and enjoyed the cool breeze.
• broaden [brɔdṇ] vt. 拓展
  Reading gives people opportunities to broaden their minds.

11. range [rendʒ] n. [C] 種類；系列　a selection of different things of a certain
    type
    A menu above the counter listed a wide range of teas for customers to choose from.

• range n. [C] 範圍　
  If there is an increase in train ticket prices, it should be in the range of twenty to fifty dollars.
• range [rendʒ] vi. 範圍包括……
  This camp is designed for children who range in age from six to ten.

12. field [fild] n. [C] 領域　a specific area of work or study
    Most of the key speakers at this international conference are experts in the field of space travel.

13. philosophy [fə lɑsəfɪ] n. [U] 哲學　the study of the nature of human life and
    thoughts
    Studying philosophy helped Sarah learn more about herself.

14. launch [lɔntʃ] vt. 發行　to allow a new product, company, or website to
    become available to the public for the first time
    The company will launch their new product in France tomorrow.

• launch vt. 發起；開始從事
  The army launched a surprise attack on the enemy yesterday.

15. collection [kə lɛkʃən] n. [C] 一堆、群、批……等　a group of things or people
    During the sale at the furniture store, a huge collection of tables and chairs was on display outside the door.

• collection n. [C] 收藏品
  Megan has a large private collection of Spider-Man comic books.
• collect [kə lɛkt] vt. 收集；收取
  We collected water samples from different rivers for our research.

16. numerous [njumərəs] adj. 許多的　many; large in number
    There are numerous hotels along the coast, so it won’t be hard to find a place to stay.

17. celebrity [sə lɛbrətɪ] n. [C] 名人　a person who is widely known or famous
    All the leading characters became international celebrities after the TV drama was broadcast worldwide.

18. fascination [ˏfæsṇ eʃən] n. [U] 著迷　a strong interest in something or someone
    Tina watched in fascination as the movie went on.

• fascination n. usually sing. 吸引力
  Pandas have always held a fascination for Anna, so a trip to the zoo was well worth it for her.
• fascinate [fæsṇˏet] vt. 使人著迷；吸引
  Amy was absolutely fascinated by the TV talk show; she didn’t even hear the telephone ring.

19. fiction [fɪkʃən] n. [U] 小說　books or stories that describe imaginary characters and events instead of actual facts
    Pride and Prejudice is one of the most famous examples of romantic fiction.

20. discuss [dɪ skʌs] vt. 探討；闡述　to share detailed opinions or ideas on a topic, either in speech or in writing
    This topic will be discussed in detail in the next chapter.

• discuss vt. 討論　
  Eva made a decision after discussing her ideas with her friends.
• discussion [dɪ skʌʃən] n. [C, U] 討論
  The couple had a long discussion about the possibility of moving to a different city. They talked for hours.
  The matter is still under discussion, so everyone has a chance to voice his or her opinion before we decide.

21. method [`mɛθəd] n. [C] 方式　a specific way to do something or process of doing something
    Ben adopted an effective method of studying and got good grades on this exam.

---

8

1. exchange [ɪks tʃendʒ] n. [C] （不同國家人民的）交流，交換（計畫）　an arrangement by which people from different countries visit each other’s homes, schools, or companies
   While taking part in a six-month exchange program in Canada, Heather improved her English as well as her French.

• exchange n. [C, U] 交換
  This meeting was held to promote an exchange of ideas and information among scientists from around the world.
  During his travels in Australia, Leo worked in exchan****ge for food and a place to stay.
• exchange [ɪks`tʃendʒ] vt. 交換
  Betty exchanged gifts with her friends at the Christmas party.

2. expect [ɪk spɛkt] vt. 預期　to hope, believe, or think that someone will do something or that something will occur in the future
   Most passengers expected that the train would be on time, but it was half an hour late.

• expectation [ˏɛkspɛk teʃən] n. [C, U] 期望；預期
  Most parents have high expectations of their children. They hope that their children can make them proud.
  The magician’s fans waited in expectation of what trick would come next.

3. shelter [ʃɛltɚ] vt. 遮蔽　to provide someone with cover or protection from the weather or danger
   Flora usually uses an umbrella to shelter herself from the sunshine.

• shelter [ʃɛltɚ] n. [C] 庇護處
  The government is planning to build a new shelter for the stray animals in the city.
  n. [U] 遮蔽
  Caught in the thunderstorm, several people took shelter from the wind and rain under the roof of a bus stop.

4. fierce [fɪrs] adj. （天氣狀況）強烈的　(of weather conditions) strong and powerful
   The weather forecast suggested that people stay indoors to avoid the fierce midday heat.

• fierce [fɪrs] adj. （動作或情感）激烈的
  There has always been fierce competition between the twins. Each is desperate to be better than the other at everything.

5. occupy [ɑkjəˏpaɪ] vt. 占據（時間或空間）　(occupied—occupied—occupying) to use up, or to take up, a certain amount of space or time
   When Joyce went shopping, finding a new dress occupied most of her time.

• occupy vt. 占領
  During World War II, most regions of Southeast Asia were occupied by Japan.
• occupation [ˏɑkjə peʃən] n. [C] 職業
  Please write your name, age, and occupation in the blanks below.

6. vehicle [viɪkḷ] n. [C] 車輛；交通工具　a machine for transporting people or things, especially a car
   Scooters are vehicles commonly seen on the roads in Taiwan.

7. temporary [tɛmpəˏrɛrɪ] adj. 臨時的；暫時的　lasting just for a short time
   People whose homes were destroyed by the earthquake can stay in a temporary shelter while their houses are being rebuilt.

8. assistant [ə sɪstənt] n. [C] 助手；助理　a person who helps someone in a higher position do a job
   Dr. Barry has hundreds of students, so he relies on a teaching assistant to help manage his classes.

• assist [ə sɪst] vt. vi. 幫助
  This newly created app assists people in finding the nearest bus stop.
  The manager is looking for a new secretary to assist with her routine work.
• assistance [ə sɪstəns] n. [U] 幫助
  When Freddy failed to find a pair of shorts in his size, a friendly clerk came to his assistance.

9. curious [kjʊrɪəs] adj. 好奇的　eager to know something
   The reporter was curious about the murder case and hoped to get as many details about it as possible.

• curiosity [ˏkjʊrɪ ɑsətɪ] n. [U] 好奇心
  Norman found a fancy old box in the basement and decided to open it out of curiosity.

10. originate [ə rɪdʒəˏnet] vi. 起源　to occur or appear for the very first time
    Fortune cookies, which are normally served at Chinese restaurants in the US, actually originated in Japan.

• origin [ ɔrədʒɪn] n. [C, U] 起源
  New York is also known as the “Big Apple,” a name said to have its origins in horse racing circles.
  The word “kindergarten” is German in origin and means “children’s garden.”
• original [ə rɪdʒənḷ] adj. 原本的
  Our original plan for the weekend was to go camping, but it was canceled due to a typhoon.

11. event[ɪ vɛnt] n. [C] 事件　a thing that occurs, especially something important
    You can learn much about the world by reading newspaper articles that discuss current events.

12. elder [ɛldɚ] n. [C] 長輩　an older person, especially someone who has considerable experience and authority
    In many African villages, elders are deeply respected for having the experience and wisdom that come with age.

• elder [ɛldɚ] adj. （家庭成員）較為年長的
  Judy’s elder sister finished school two years ahead of her and currently works as a nurse.
• elderly [ɛldɚlɪ] adj. 年紀大的
  Two friendly teenagers assisted the elderly lady in crossing the street safely.

13. neighborhood [nebɚˏhʊd] n. [C] 鄰近地區　the area which someone or something is in
    It will be convenient for us to exercise after the new sports center in our neighborhood opens.

14. cooperate [ko ɑpəˏret] vi. 合作　to work with someone in order to complete a task or achieve a goal
    Fast-food restaurants often cooperate with toy makers in providing toys to attract more children.

• cooperation [koˏɑpə reʃən] n. [U] 合作
  On Saturday, the zoo will be hosting a special outdoor event in cooperation with a science museum.

15. arrange [ə rendʒ] vt. vi. 安排　to organize or plan something
    Mike has arranged a trip to Japan with his family during Chinese New Year.
    If necessary, the hotel can arrange for a shuttle to take its guests to and from the station.

• arrangement [ə rendʒmənt] n. [C] 安排
  Before they set out, the couple had made many arrangements for their journey across the US, including booking flights, hotels, and trains.

16. relax [rɪ læks] vi. 放鬆　to rest by doing something pleasant
    With a whole day to spend at the beach, the family could just relax in the sun and take it easy.

17. container [kən tenɚ] n. [C] 容器　an empty object, such as a bottle or box, made for holding things
    If you want to heat up food in the microwave, be sure not to put it in a plastic container.

• contain [kən ten] vt. 包含
  When Janice opened the envelope, she found that it contained a handmade card from her best friend.

18. stroll [strol] vi. 散步　to walk slowly and easily, usually simply to relax or to look around
    Hand in hand, the young lovers strolled along the lakeside without a care in the world.

• stroll [strol] n. [C] 散步
  There’s still an hour before the movie begins, so why not go for a nice str****oll in the park first?

19. aspect [æspɛkt] n. [C] 方面　a certain feature or part of a situation, idea, problem, etc.
    Location is an important aspect of tea farming. Different places can produce totally different teas.

20. spirit [`spɪrɪt] n. sing. 基本精神；本質　the unifying nature or quality of something
    All of these baseball players have a strong team spirit.

• spirit n. [U] 精神；心靈
  Although Kate’s parents couldn’t attend her first piano concert in person, she felt they were with her in spirit.
  spiritual [spɪrɪtʃʊəl] adj. 精神上的
  The Pope is the spiritual leader of Catholics around the world.

---

9

1. general [dʒɛnərəl] adj. 一般的；非專門的　not limited or specialized in usage
   Eagles, owls, chickens, and ducks all fall under the general term of “birds.”

• general adj. 普遍的；一般的
  In general, the air becomes fresher the farther you move away from the big city.

2. derive [də raɪv] vt. 起源於　to be born out of or come from something else
   The English word “language” is derived from the Latin word for “tongue.”

• derive vt. 得到；獲得
  Mrs. Adams derived a lot of pleasure from seeing all the guests enjoy her chocolate pudding so much.

3. feature [fitʃɚ] vt. 以……為特色　to include someone or something as an important part
   This company’s latest smartphone features a better camera than any other phone on the market.

• feature [fitʃɚ] n. [C] 特色；特點
  Rain and fog are two common features of the weather in England.

4. gossip [gɑsəp] n. [U] 流言；八卦　discussion or rumors about other people’s personal affairs, especially when they are absent
   Lately, lots of gossip about the actor’s affair has been going around in show business.

• gossip [gɑsəp] vi. 散播流言；說八卦
  Ellen didn’t feel comfortable gossiping about Bart’s new wife. To her, it was wrong to discuss other people’s private lives.

5. reveal [rɪ vil] vt. 洩漏；透露　to let out a secret or to make something known for the first time
   Andy didn’t want to reveal his travel plans to anyone but his best friend.

6. release [rɪ lis] vt. 公開發行　to make something available in public for the first time
   When the final novel in the series was recently released, fans waited in line for hours to get a copy.

• release vt. 釋放
  Once the bear recovered from its injuries, the park’s staff released it from its cage and sent it back into the wild.
• release [rɪ lis] n. [U] 公開發行
  Ever since the release of its first album, the band has become increasingly popular.
• release n. [U] 釋放；排放
  The factory was fined due to its release of harmful wastes into the river.

7. chase [tʃes] vt. vi. 追逐　to pursue someone or something in order to catch them
   After chasing the fox for almost an hour, the exhausted dog gave up and left.
   In his dream, Rusty was running for his life as a huge and fierce tiger chased after him.

• chase [tʃes] n. [C] 追逐
  The police finally arrested a suspected car thief after a long highspeed chase.

8. brand [brænd] n. [C] 品牌　a type of product that has its own name and is made by a particular company
   When it comes to soft drinks, Coca-Cola is the most famous brand.

9. image [ɪmɪdʒ] n. [C] 影像　a visual representation of someone or something, usually seen in a mirror or on a screen
   Baby Ruth was very curious when she first noticed her own image in the mirror.

• image n. [C] 形象
  The actress tried to improve her public image by participating in charity events.

10. edit [ɛdɪt] vt. 編輯　to change something in order to improve or correct it
    It is important to carefully edit an essay before handing it in.

• edition [ɪ dɪʃən] n. [C] 版本
  The publisher has corrected several mistakes and added a new article in the book’s most recent edition.

11. modify [mɑdəˏfaɪ] vt. 修改　to make small changes to something to ensure that it looks, works, or fits better
    The engineer modified the design to improve the performance of the system.

• modification [ˏmɑdəfə keʃən] n. [C, U] 修改
  Adam made a modification to the bicycle so that his child can learn to ride it safely.
  Most men’s suits require modification before they can fit perfectly.

12. digitally [dɪdʒɪtəlɪ] adv. 數位地　using computer technology to record, store, or send data on an electronic device
    You can store the photos digitally on the phone and view them directly on the screen.

• digital [dɪdʒɪtḷ] adj. 數位的
  In the digital age, no one can live without the computer and the Internet.

13. combine [kəm baɪn] vt. vi. 結合　to use or join two or more things together
    To make the sauce for the fish, simply combine some lemon juice with a splash of vinegar.
    When the two chemicals combine, they will release harmful gases.

• combination [ˏkɑmbə neʃən] n. [C, U] 結合
  It was a combination of hard work and dedication that allowed the foundation to become so successful worldwide.
  Kelly loved the performance for its perfect combination of music, dance, and acting.

14. standard [stændɚd] adj. 標準的　of average quality rather than having special features
    Several standard hotel rooms are available at a cheaper rate, but they don’t have a balcony with an ocean view.

• standard [stændɚd] n. [C, U] 標準
  Elsa’s parents set a really high standard for her, so she always struggles to meet their expectations.
  The customer service of the bank wasn’t up to current standard, so the manager provided further training for all the staff.

15. widespread [waɪd͵sprɛd] adj. 廣泛的　common or occurring among large numbers of people or over a large area
    The typhoon has caused widespread damage in the area.

16. usage [jusɪdʒ] n. [U] （語彙的）用法　the way in which the words of a language are used and understood
    The earliest recorded usage of the word “dude” dates back to the 1880s.

17. constantly [kɑnstəntlɪ] adv. 持續地　without stopping or all the time
    To learn a foreign language well, you have to practice it constantly.

• constant [kɑnstənt]adj. 持續的；不斷的
  The constant noise throughout the night made it hard for Chris to fall asleep.

18. alternative [ɔl tɝnətɪv] adj. 另類的；非傳統的　not the same as the common, usual, or traditional way
    When doctors failed to cure his cancer, Lance started researching alternative medicines.

• alternative adj. 替代的
  Emma soon got tired of taking the bus to work and started looking for alternative ways to get to her office.
• alternative [ɔl tɝnətɪv] n. [C] 選擇；替代方案
  The weather was so bad that the teenagers had no alternative but to cancel their camping trip.

19. existing [ɪg zɪstɪŋ] adj. 現有的；現存的　already found or in use at present
    Mark’s goal is to improve his existing class score average from seventy percent to eighty percent next semester.

• exist [ɪg zɪst] vi. 存在
  Mike believes that aliens really exist, but his brother doesn’t think they are real.
• existence [ɪg zɪstəns] n. [U] 存在
  Scientists have many theories about how the universe came into existence.

---

片語

7

1. as well as　和；除了……以外　in addition to
   Each student will be given a textbook as well as a notebook before the class.
2. for free　免費　not costing anything
   Ten lucky winners can go to the concert for free. It will not cost a cent!
3. at present　目前；現在　now
   Clive used to like comedies, but at present he’s more interested in horror movies.
4. give…a try　嘗試……　to experience or attempt to do something
   Penny decided to give green tea a try to see how it tasted.
5. broaden one’s horizons　拓展（某人的）視野　to learn more or to open one’s
   mind, especially by trying new things or visiting new places
   Hank learned so much during his trip across Europe. It really broadened his horizons.

---

8

1. take part in　參加　to participate in; to be involved in
   Over ten thousand people from around the country took part in the singing contest.
2. take place　舉行；發生　to happen, especially after being arranged
   The FIFA World Cup takes place every four years.
3. come about　發生　to happen, especially in a way that is not planned
   This book explains how extreme weather on earth has come about.
4. help (…) out　幫忙　to assist others, especially when they are not able to do something themselves
   The breakfast shop is always busy on weekends, so the owner’s sons usually help him out.
5. hand out　發放　to give things to individual members of a group
   As Mrs. Brink concluded the day’s lesson, she handed out a reading list to all the students.

---

9

1. take on　開始具有　to start to have or show a specific quality
   As soon as Darren grew a beard, he took on the appearance of an older man.
2. later on　之後　sometime after that, further into the future, or at a later point in time
   The family began their European holiday in Spain. Later on, they visited France and Germany.
3. in the beginning　起初　at the start or at first
   In the beginning, Jasmine didn’t like Kenny. However, they became great friends after they got to know each other better.
4. too…to…　太……而無法……　to such a degree that something is not
   possible
   Nora tried to calm Kevin down, but he was too angry to listen to anybody.
5. play a/an…role (in)　扮演……的角色　to provide a certain function
   It is obvious that learners’ motivation plays an important role in learning English.
6. think up　想出　to come up with or imagine a new idea, story, method, or solution
   Eva doesn’t want to go to Wayne’s party, so she needs to think up a good excuse.

---

補充單字

7

TED Talks [tɛd tɔks]　n. TED演講（不同領域的專家以演講形式於TED平台與大眾分享資訊）
social networking site [soʃəl nɛtwɝkɪŋ saɪt]　n. [C] 社交網站
platform [plætˏfɔrm]　n. usually sing. （公開表達看法的）機會
slogan [slogən]　n. [C] 口號；標語
upload [ʌp lod]　vt. 上傳
insight [ɪnˏsaɪt]　n. [C] 見解
chef [ʃɛf]　n. [C] 主廚
Jamie Oliver [dʒemi ɑləvɚ]　n. 傑米•奧利佛
James Cameron [dʒemz kæmərən]　n. 詹姆斯•卡麥隆
Aliens [ elɪənz]　n. 《異形2》
Avatar [ævəˏtɑr]　n. 《阿凡達》
blockbuster [blɑkˏbʌstɚ]　n. [C] 賣座鉅片
Bill Gates [bɪl gets]　n. 比爾•蓋茲
co-founder [koˏfaʊndɚ]　n. [C] 共同創辦人
Microsoft [ maɪkrosɔft]　n. 微軟
Ebola [ɪ bolə]　n. 伊波拉

---

8

ban-doh [bænˏdɔ]　n. [C] （臺語）辦桌
authentic [ɔ θɛntɪk] 　adj. 道地的；真正的
banquet [bæŋkwɪt]　n. [C] 宴會
tent [tɛnt]　n. [C] 帳篷
platter [plætɚ]　n. [C] 大淺盤
utensil [ju tɛnsḷ]　n. [C] （廚房或用餐的）器具
leftovers [lɛftˏovɚz]　n. pl. 剩菜
folks [foks]　n. pl. 人們

---

9

eponym [ɛpəˏnɪm]　n. [C] 借名成字（以人名、品牌名稱來命名的方式）
paparazzi [͵pɑpə rɑtsɪ]　n. pl. 狗仔隊（單數形為paparazzo）
Photoshop [ fotoˏ ʃɑp]　n. Photoshop（一款由Adobe開發和發行的影像處理軟體）
verb [vɝb]　n. [C] 動詞
Paparazzo [ˏpɑpə rɑtso]　n. 義大利名（為一部義大利電影的角色名稱）
Italian [ɪ tæljən]　adj. 義大利的
La Dolce Vita [͵lɑ dɔtʃɚ vitə]　n. The Sweet Life《甜蜜的生活》（一部1960年上映的義大利電影）
plural [ plʊrəl]　n. [C] 複數
software [sɔft͵wɛr]　n. [U] 軟體
Adobe Inc. [ə dobɪ ɪŋk]　n. Adobe公司（為美國一家跨國電腦軟體公司）

---

文法

7

Honey, I’m sorry to have kept you waiting for so long.(1)
Leave me alone!(2)
Listen, honey. I’d gotten this for you, but I left it at home.(3) So I went back and…
Yes, I do!
在此語境中，句(1)Shrek對Fiona「等待太久」而感到抱歉，句(2) Fiona想要「獨自一人」，句(3) Shrek發現戒指「留在家裡」，因此使用「keep/leave/find + O + V-ing/p.p./adj./prep.」的句型，來帶出該動詞後面受詞的附帶狀態，使語意更完整。
S + keep/leave/find + O + V-ing/p.p./adj./prep…..
此句型用於說明keep/leave/find三個動詞後面所接受詞的附帶狀態，表達「使／任由／發現……處於某種狀態」，使其語意更完整。
keep/leave/find後面須接一個名詞當受詞，受詞後面可接：
現在分詞：表主動或持續進行的動作
Don’t leave your car running while you fill it with gas.
過去分詞：表被動或已經完成動作
I was surprised to find the door unlocked when I got home.
形容詞：表狀態
It’s so hot in this room. Please keep the windows open.
介系詞／介系詞片語：表狀態或位置
Hank woke up and found his dog beside his bed.

---

8

LeBron James May Return from Ankle Injury Next Week

After taking a long break, LeBron James has finally recovered from his ankle sprain and is expected to be back on court next week.

在此語境中，新聞的副標題主要報導LeBron James傷後將重返球場的消息，而他長時間休養則是背景資訊，因此使用分詞構句的句型，以分詞表達背景資訊，進而襯托主要訊息。

(Conj.) V-ing/p.p…, S + V….

1. 此句型是由從屬連接詞（when、while、after、before、because、although 等）連接的從屬子句簡化而成的分詞構句，當兩個子句主詞相同時，從屬子句的簡化步驟如下：
   (1) 省略連接詞與主詞。
   (2) 將動詞改為分詞，主動用現在分詞（V-ing），被動用過去分詞（p.p.）。
   (3) 若要簡化的子句為否定句，則在分詞前加上not。
   When she cleaned her son’s room, Rita came across an old family photo.

→ Cleaning her son’s room, Rita came across an old family photo.
Because it didn’t know how to get out of the cage, the dog barked angrily.

→ Not knowing how to get out of the cage, the dog barked angrily.
2. 將從屬連接詞省略後，若會造成語意不清，則可保留從屬連接詞。
Before going to her office, Amanda always gets a cup of coffee at the convenience store.（例句中的兩個動作有先後順序之分，為幫助讀者正確判讀句意，故保留連接詞before。）
3. 分詞構句主要是讓從屬子句更為精簡，經簡化後，分詞的功能為提示背景資訊或說明主詞特性，進而凸顯主要子句的內容。
Although born without arms and legs, Nick Vujicic has overcome all his challenges and lives a life of joy and fulfillment.

---

9

Spain	UK	Iceland
It is believed that eating twelve grapes as the clock strikes midnight on New Year’s Eve will bring you twelve months of good luck.	It is thought that saying “white rabbits” on the first day of the month before saying anything else will bring you good luck.	If you move to a new house, make sure you do so on a rainy day. It is said that this will make you wealthy.

在此語境中，三個國家各自有可帶來好運的習俗，皆為眾人相信或口耳相傳的想法及說法，因此使用「It is said/believed that…」的句型。
It’s said/believed/reported/…that + S + V…

1. 此句型用於表達客觀的事實或眾人的說法及意見，常出現於此句型的動詞有 say、believe、report 等，表示「據說／據信／據報導⋯⋯」。句型中「it」為虛主詞，代替真正的主詞「that + S + V」。
   It is believed that owning a pet helps reduce stress.
2. 此句型常出現於新聞報導及學術性文章，搭配使用的動詞多帶有報告或陳述性質，此類動詞有 report、show、indicate、expect 等。
   It is reported that thirteen people have been killed in the gunfire.
   It has been shown that in face-to-face interactions, fifty-five percent of the communication takes place through body language.