The nuclear energy levels of mirror nuclei are similar. Using this empirical fact
alone, the nuclear force can be said to be independent of which one of the following
properties of the nucleons?
Options:
(A) Mass
(B) Spin
(C) Charge
(D) Parity
Official Answer Key:
C
Step-by-Step Solution & Explanation
### **Official Solution & Step-by-Step Derivation (GATE PH 2025 Q.20)**
**1. Nuclear Physics & Mirror Nuclei**:
- Mirror nuclei are isobaric pairs $(Z_1, N_1)$ and $(Z_2, N_2)$ where the number of protons and neutrons are mutually interchanged:
$Z_1 = N_2, \qquad N_1 = Z_2$
*(e.g. $^3_1\text{H}$ and $^3_2\text{He}$, or $^{15}_7\text{N}$ and $^{15}_8\text{O}$)*.
**2. Physical Analysis**:
- In mirror nuclei, the total number of nucleon-nucleon pairs is identical, with the only distinction being the swap of $(n-n)$ pairs with $(p-p)$ pairs.
- After calculating and subtracting the classical Coulomb repulsion energy between protons $\Delta E_C$, the experimental nuclear energy level spectra of mirror nuclei match with extraordinary precision.
- This empirical equality proves that the nuclear strong interaction between two neutrons ($n-n$) is identical in magnitude and form to the nuclear interaction between two protons ($p-p$).
- Hence, the nuclear force is **charge-independent**.
**3. Official Verification**:
The verified official IIT answer is **Option (C)** (`Charge`).
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