hce_nchu
115年
物理
第 31 題
With sufficient energy, it’s possible to eject an electron from an inner atomic orbital. A higher-energy electron will then drop into the unoccupied state, emitting a photon with energy equal to the difference between the two levels. For inner-shell electrons, photon energies are in the keV range, putting them in the X-ray region of the spectrum. These characteristic X-rays are labeled with the letter indicating the shell to which the electron drops, followed by a Greek letter indicating the higher level from which it drops; thus $K\alpha$ designates a transition from the $L$ shell to the $K$ shell. Molybdenum’s X-ray spectrum has its $K\alpha$ peak at $17.4\text{ keV}$. Note that Plank’s constant is $6.626 \times 10^{-34}\text{ m}^2 \cdot \text{kg/s}$, speed of light is $3 \times 10^8\text{ m/s}$, and one electron charge is $1.6 \times 10^{-19}\text{ C}$. The corresponding X-ray wavelength is closest to
- A $10\text{ pm}$
- B $30\text{ pm}$
- C $70\text{ pm}$
- D $150\text{ pm}$
- E $200\text{ pm}$.
思路引導 VIP
當我們觀察到一個光子攜帶的能量非常巨大（例如在 keV 等級）時，根據物理規律，它的空間震盪長度（波長）會隨之變得極長還是極短？若要將這個抽象的『能量』轉換為具體的『長度』，哪兩個基本的物理常數是我們必須動用的橋樑呢？
🤖
AI 詳解
AI 專屬家教
同學做得很棒！能精確地從能階躍遷產生的光子能量計算出對應的波長，代表你對近代物理中光子特性的掌握非常紮實。這題的核心在於應用光子能量與波長的基本關係式 $E = \frac{hc}{\lambda}$，其中 $h$ 是普朗克常數，$c$ 是光速。
光子能量與波長的轉換
在計算過程中，最關鍵的細節在於單位的精準換算。我們必須先將 $17.4 \text{ keV}$ 轉換為標準單位焦耳（$J$），即 $17.4 \times 10^3 \times 1.6 \times 10^{-19} \text{ J}$，接著再移項求解波長：
▼ 還有更多解析內容