Question

An electron microscope is used to probe the atomic arrangements to a resolution of 5 \AA. What should be the electric potential to which the electrons need to be accelerated?

• A. 2.5 V
• B. 5 V
• C. 2.5 kV
• D. 5 kV

Hint:

Electron wavelength decreases with higher accelerating voltage: \(\lambda = \frac{12.27}{\sqrt{V}}\) \AA.

Answer 1

The Correct Option is B

Step 1: Use de Broglie wavelength relation.
For electron accelerated by potential \(V\), de Broglie wavelength is:
\[ \lambda = \frac{12.27}{\sqrt{V}} \, \text{\AA} \]
Step 2: Resolution required means wavelength should be comparable.
Given resolution \(\lambda = 5\) \AA.
Step 3: Substitute in formula.
\[ 5 = \frac{12.27}{\sqrt{V}} \]
\[ \sqrt{V} = \frac{12.27}{5} = 2.454 \]
\[ V = (2.454)^2 \approx 6.02 \, \text{V} \]
Step 4: Choose nearest option.
Closest option to 6 V is 5 V.
Final Answer:
\[ \boxed{\text{(B) 5 V}} \]