Question

Assertion (A): An alpha particle is moving towards a gold nucleus. The impact parameter is maximum for the scattering angle of 180°. % Reason (R) Reason (R): The impact parameter in an alpha particle scattering experiment does not depend upon the atomic number of the target nucleus.

• A. If both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
• B. If both Assertion (A) and Reason (R) are true and Reason (R) is not the correct explanation of Assertion (A).
• C. If Assertion (A) is true but Reason (R) is false.
• D. If both Assertion (A) and Reason (R) are false.

Hint:

In Rutherford scattering, the maximum scattering angle of 180° corresponds to the largest impact parameter, which occurs when the alpha particle is deflected directly back.

Answer 1

The Correct Option is D

Analysis of Assertion (A):
The impact parameter (\(b\)) signifies the closest approach distance of an alpha particle to a gold nucleus if no electrostatic forces were present. In Rutherford scattering, the relationship between the impact parameter (\(b\)) and the scattering angle (\(\theta\)) is: \[b \propto \cot\left(\frac{\theta}{2}\right)\] When the scattering angle is \(\theta = \SI{180}{\degree}\): \[\cot\left(\frac{\SI{180}{\degree}}{2}\right) = \cot(\SI{90}{\degree}) = 0\] This indicates that for a scattering angle of \(\SI{180}{\degree}\), the impact parameter (\(b\)) is minimal, approaching zero. Consequently, Assertion (A) is false.
Analysis of Reason (R):
The impact parameter (\(b\)) is inversely proportional to the atomic number (\(Z\)) of the target nucleus, as shown by: \[b \propto \frac{1}{Z}\] This implies that as the atomic number of the target nucleus increases, the impact parameter decreases. Therefore, Reason (R) is false.
Conclusion:

Assertion (A) is false.

Reason (R) is false.
Thus, the correct answer is: \[\boxed{\text{Both Assertion (A) and Reason (R) are false.}}\]