When a `beta^(-)` particle is emitted from a nucleus, the neutrons-proton ratio:

Options

A. os decreased
B. is increased
C. remains the same
D. may in increases or decreases

Answer

To solve the question regarding the change in the neutron-proton ratio when a beta particle is emitted from a nucleus, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Beta Decay**:
- In beta decay, a beta minus particle (β⁻) is emitted from a nucleus. This process involves a neutron in the nucleus being converted into a proton, while emitting an electron (the beta particle) and an antineutrino.

2. **Identifying the Nucleus Before Decay**:
- Let’s denote the original nucleus as X, which has an atomic number Z and a mass number A. The number of neutrons (N) in nucleus X can be calculated as:
\[ N = A - Z \]

3. **Identifying the Nucleus After Decay**:
- After the emission of a beta particle, the nucleus transforms into a new nucleus Y. The atomic number of Y becomes \( Z + 1 \) (since one neutron is converted into a proton), while the mass number remains the same (A). Thus, for nucleus Y:
\[ N' = A - (Z + 1) = A - Z - 1 \]
- The number of protons in nucleus Y is:
\[ Z' = Z + 1 \]

4. **Calculating the Neutron-Proton Ratios**:
- The neutron-proton ratio for nucleus X (before decay) is:
\[ \text{Ratio}_X = \frac{N}{Z} = \frac{A - Z}{Z} \]
- The neutron-proton ratio for nucleus Y (after decay) is:
\[ \text{Ratio}_Y = \frac{N'}{Z'} = \frac{A - Z - 1}{Z + 1} \]

5. **Analyzing the Change in Ratio**:
- To determine how the ratio changes, we can compare \(\text{Ratio}_X\) and \(\text{Ratio}_Y\):
- The numerator of \(\text{Ratio}_Y\) decreases by 1 compared to \(\text{Ratio}_X\).
- The denominator of \(\text{Ratio}_Y\) increases by 1 compared to \(\text{Ratio}_X\).
- Since the numerator decreases and the denominator increases, the overall ratio \(\text{Ratio}_Y\) will be less than \(\text{Ratio}_X\).

6. **Conclusion**:
- Therefore, the neutron-proton ratio decreases when a beta minus particle is emitted from a nucleus.

### Final Answer:
The neutron-proton ratio **decreases** when a beta minus particle is emitted from a nucleus.

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