Question

A parallel beam of fast moving electrons is incident normally on a narrow slit. A screen is placed at a large distance from the slit. If the speed of the electrons is increased, which of the following statement is correct?

• A. diffraction pattern is not observed on the screen in the case of electrons
• B. the angular width of the central maximum of the diffraction pattern will increase
• C. the angular width of the central maximum will decrease
• D. the angular width of the central maximum will remain the same

Hint:

Higher electron speed \(\Rightarrow\) smaller de Broglie wavelength \(\Rightarrow\) smaller diffraction spread.

Answer 1

The Correct Option is C

Step 1: Use de Broglie wavelength for electrons.
\[ \lambda = \frac{h}{p} = \frac{h}{mv} \]
Step 2: Effect of increasing speed.
If \(v\) increases, momentum \(p=mv\) increases, so de Broglie wavelength decreases:
\[ v \uparrow \Rightarrow \lambda \downarrow \]
Step 3: Diffraction angular width relation.
For single slit diffraction:
\[ \theta \approx \frac{\lambda}{a} \]
So if \(\lambda\) decreases, \(\theta\) decreases.
Step 4: Conclusion.
Thus, the angular width of central maximum decreases when electron speed increases.
Final Answer:
\[ \boxed{\text{(C) angular width decreases}} \]