The triad of nuclei that is isotonic is

Options

A. `._(1)H^1and _1H^2 and _1H^3`
B. `._(92)^(235)U,._(92)^(40)U and ._(92)^(238)U`
C. `._(18)^(40)Ar,._(19)^(40)K and ._(20)^(40)Ca`
D. `._(6)^(14)C,._(7)^(15)N and ._(8)^(16)O`

Answer

To determine the triad of nuclei that is isotonic, we need to follow these steps:

### Step 1: Understand the Definition of Isotonic Nuclei
Isotonic nuclei are nuclei that have the same number of neutrons (N) but different numbers of protons (Z). The relationship between atomic mass (A), atomic number (Z), and the number of neutrons (N) is given by:
\[ N = A - Z \]

### Step 2: Analyze the Given Options
We need to check each option to see if the nuclei in that option have the same number of neutrons (N) while having different atomic numbers (Z).

### Step 3: Calculate Neutrons for Each Nucleus
For each nucleus in the options provided, we will calculate the number of neutrons using the formula \( N = A - Z \).

1. **Option 1**:
- Nucleus 1: \( A_1, Z_1 \) → \( N_1 = A_1 - Z_1 \)
- Nucleus 2: \( A_2, Z_2 \) → \( N_2 = A_2 - Z_2 \)
- Nucleus 3: \( A_3, Z_3 \) → \( N_3 = A_3 - Z_3 \)
- Check if \( N_1 = N_2 = N_3 \)

2. **Option 2**:
- Repeat the same calculations for the nuclei in this option.

3. **Option 3**:
- Repeat the same calculations for the nuclei in this option.

4. **Option 4**:
- Nucleus 1: \( ^{14}_{6}C \) → \( N = 14 - 6 = 8 \)
- Nucleus 2: \( ^{15}_{7}N \) → \( N = 15 - 7 = 8 \)
- Nucleus 3: \( ^{16}_{8}O \) → \( N = 16 - 8 = 8 \)
- Here, \( N_1 = N_2 = N_3 = 8 \)

### Step 4: Conclusion
After calculating the number of neutrons for each option, we find that only in option 4 do all three nuclei have the same number of neutrons (8). Therefore, the triad of nuclei that is isotonic is:

**Answer: Option 4 (14, 6, C; 15, 7, N; 16, 8, O)**

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