Question

Calculate the de Broglie wavelength of an electron accelerated through a potential of \(100\,\text{V}\).

• A. \(1.227\,\text{\AA}\)
• B. \(0.612\,\text{\AA}\)
• C. \(2.45\,\text{\AA}\)
• D. \(3.12\,\text{\AA}\)

Hint:

For electrons accelerated through potential \(V\): \[ \lambda=\frac{12.27}{\sqrt{V}} \text{ \AA} \] This shortcut formula is commonly used in quantum mechanics problems.

Answer 1

The Correct Option is A

Step 1: Understanding the Question:
The task is to find the de Broglie wavelength associated with an electron that has been given kinetic energy by a 100V accelerating potential.
Step 2: Key Formula or Approach:
For an electron accelerated through potential \(V\), the de Broglie wavelength \(\lambda\) is given by the shortcut formula:
\[ \lambda = \frac{12.27}{\sqrt{V}} \text{ \AA} \]
Step 3: Detailed Explanation:
1. Identify the given values:
Accelerating potential, \(V = 100 \text{ V}\).
2. Apply the formula:
\[ \lambda = \frac{12.27}{\sqrt{100}} \text{ \AA} \]
3. Perform calculation:
\[ \sqrt{100} = 10 \]
\[ \lambda = \frac{12.27}{10} \text{ \AA} \]
\[ \lambda = 1.227 \text{ \AA} \]
Step 4: Final Answer:
The de Broglie wavelength of the electron is \(1.227 \text{ \AA}\).