Which among the following nuclides `"is"//"are"` likely to be stable?

Options

A. `._(49)In^(114)`
B. `._(12)Mg^(24)`
C. `._(48)Cd^(114)`
D. `._(15)P^(30)`

Explanation

To determine which of the given nuclides (indium, magnesium, cadmium, and phosphorus) are likely to be stable, we will calculate the neutron-to-proton (n/p) ratio for each nuclide. The stability of a nuclide is often indicated by this ratio, with certain ranges suggesting stability.

### Step-by-Step Solution:

1. **Identify the Nuclides and Their Atomic Numbers**:
- Indium (In): Atomic number 49
- Magnesium (Mg): Atomic number 12
- Cadmium (Cd): Atomic number 48
- Phosphorus (P): Atomic number 15

2. **Determine the Number of Neutrons**:
- For each nuclide, we need to know the mass number (A) to calculate the number of neutrons (N). The number of neutrons can be calculated using the formula:
\[ N = A - Z \]
where \(Z\) is the atomic number (number of protons).

- For Magnesium (Mg):
- Mass number (A) = 24 (common isotope)
- Number of neutrons (N) = 24 - 12 = 12

- For Cadmium (Cd):
- Mass number (A) = 112 (common isotope)
- Number of neutrons (N) = 112 - 48 = 64

- For Indium (In):
- Mass number (A) = 115 (common isotope)
- Number of neutrons (N) = 115 - 49 = 66

- For Phosphorus (P):
- Mass number (A) = 31 (common isotope)
- Number of neutrons (N) = 31 - 15 = 16

3. **Calculate the Neutron-to-Proton Ratio (n/p)**:
- For each nuclide, calculate the n/p ratio:

- Magnesium (Mg):
\[ n/p = \frac{N}{Z} = \frac{12}{12} = 1 \]

- Cadmium (Cd):
\[ n/p = \frac{N}{Z} = \frac{64}{48} \approx 1.33 \]

- Indium (In):
\[ n/p = \frac{N}{Z} = \frac{66}{49} \approx 1.35 \]

- Phosphorus (P):
\[ n/p = \frac{N}{Z} = \frac{16}{15} \approx 1.07 \]

4. **Analyze the Ratios for Stability**:
- Generally, stable nuclides have n/p ratios close to 1 for lighter elements, and slightly higher for heavier elements.
- Magnesium (n/p = 1) and Cadmium (n/p ≈ 1.33) fall within the stable range.
- Indium (n/p ≈ 1.35) and Phosphorus (n/p ≈ 1.07) also show ratios that suggest potential stability, but Indium is heavier and may not be as stable.

5. **Conclusion**:
- Based on the neutron-to-proton ratios, Magnesium and Cadmium are likely to be stable nuclides. Indium and Phosphorus may also be stable, but their stability is less certain compared to Magnesium and Cadmium.

### Final Answer:
Magnesium (Mg) and Cadmium (Cd) are likely to be stable nuclides.