Question

For an atomic nucleus with atomic number \( Z \) and mass number \( A \), which of the following is (are) correct?

• A. Nuclear matter and nuclear charge are distributed identically in the nuclear volume.
• B. Nuclei with \( Z>83 \) and \( A>209 \) emit \( \alpha \)-radiation.
• C. The surface contribution to the binding energy is proportional to \( A^{2/3} \).
• D. \( \beta \)-decay occurs when the proton to neutron ratio is large, but not when it is small.

Hint:

In nuclear physics, heavy nuclei (with \( Z>83 \)) often undergo \( \alpha \)-decay to achieve a more stable configuration, and the surface contribution to binding energy scales with \( A^{2/3} \).

Answer 1

The Correct Option is A, B, C

Step 1: Understanding the properties of atomic nuclei.
Nuclei with large atomic numbers \( Z \) and mass numbers \( A \) typically undergo \( \alpha \)-decay due to instability caused by a high neutron-to-proton ratio. This is a common property of heavy nuclei. Option (B) is correct based on this understanding. Additionally, the surface contribution to the binding energy in a nucleus is proportional to \( A^{2/3} \), which is well-established in nuclear physics and makes option (C) correct. The other options are less accurate for the specific scenario.
Step 2: Conclusion.
Thus, the correct answers are options (B) and (C).