Question

In a Rutherford scattering experiment, when a projectile of charge \( Z_1 \) and mass \( M_1 \) approaches a target nucleus of charge \( Z_2 \) and mass \( M_2 \), the distance of closest approach is \( r_0 \). The energy of the projectile is:

• A. Directly proportional to \( Z_1Z_2 \)
• B. Inversely proportional to \( Z_1 \)
• C. Directly proportional to mass \( M_1 \)
• D. Directly proportional to \( M_1 \times M_2 \)

Hint:

For Rutherford scattering:
- The closest approach distance depends on charge and energy.
- Higher charge means stronger repulsion, requiring more energy.

Answer 1

The Correct Option is A

Step 1: The distance of closest approach is given by:
\[ r_0 = \frac{1}{4\pi\epsilon_0} \frac{Z_1 Z_2 e^2}{KE} \]
Step 2: Since \( KE \propto \frac{Z_1 Z_2}{r_0} \), we conclude:
\[ KE \propto Z_1 Z_2 \]