Question

Identify the correct statement(s) regarding nuclei:

• A. The uncertainty in the momentum of a proton in a nucleus is roughly \( 10^5 \) times the uncertainty in the momentum of the electron in the ground state of the Hydrogen atom
• B. The volume of a nucleus grows linearly with the number of nucleons in it
• C. The energy of \( \gamma \) rays due to de-excitation of a nucleus can be of the order of MeV
• D. \( ^{56}\text{Fe} \) is the most stable nucleus

Hint:

In nuclear physics, the energy of \( \gamma \)-ray transitions is typically in the MeV range, corresponding to the energy released during nuclear de-excitation.

Answer 1

The Correct Option is A, B, C, D

Step 1: Analyze each statement.
(A) The uncertainty in the momentum of a proton in a nucleus is roughly \( 10^5 \) times the uncertainty in the momentum of the electron in the ground state of the Hydrogen atom: This is incorrect. The momentum uncertainty of the proton is much higher than that of the electron, but not by a factor of \( 10^5 \).
(B) The volume of a nucleus grows linearly with the number of nucleons in it: This is an approximation, but the volume of a nucleus grows roughly as \( A^{1/3} \), where \( A \) is the mass number, not linearly with the number of nucleons.
(C) The energy of \( \gamma \) rays due to de-excitation of a nucleus can be of the order of MeV: This is correct. The energy released during the de-excitation of a nucleus often lies in the range of MeV.
(D) \( ^{56}\text{Fe} \) is the most stable nucleus: This is incorrect. \( ^{56}\text{Fe} \) is one of the most stable nuclei, but not necessarily the most stable in all conditions. The most stable nucleus is generally the one with the highest binding energy per nucleon.
Step 2: Final Answer.
Therefore, the correct statement is (C).