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 (\(b\)) is the perpendicular distance between the path of the alpha particle and the center of the gold nucleus if no force acted on the alpha particle. The relationship between the impact parameter (\(b\)) and the scattering angle (\(\theta\)) in Rutherford scattering is given by:
\[ b \propto \cot\left(\frac{\theta}{2}\right) \] For \(\theta = \SI{180}{\degree}\):
\[ \cot\left(\frac{\SI{180}{\degree}}{2}\right) = \cot(\SI{90}{\degree}) = 0 \] This means the impact parameter (\(b\)) is minimum (close to zero) for a scattering angle of \SI{180}{\degree}. Therefore, Assertion (A) is false.
Analysis of Reason (R):
The impact parameter (\(b\)) depends on the atomic number (\(Z\)) of the target nucleus. The relationship is given by:
\[ b \propto \frac{1}{Z} \] This means the impact parameter decreases as the atomic number of the target nucleus increases. Therefore, Reason (R) is false. Conclusion:

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