Which of the following nuclei is unstable?

Options

A. `._(5)B^(10)`
B. `._(4)Be^(10)`
C. `._(7)N^(14)`
D. `._(8)O^(16)`

Answer

To determine which of the given nuclei is unstable, we will calculate the neutron-to-proton (n/p) ratio for each nucleus. Generally, a higher n/p ratio indicates instability.

### Step-by-Step Solution:

1. **Identify the Nuclei and Their Mass and Atomic Numbers:**
- Boron: Mass number = 10, Atomic number = 5
- Beryllium: Mass number = 10, Atomic number = 4
- Nitrogen: Mass number = 14, Atomic number = 7
- Oxygen: Mass number = 16, Atomic number = 8

2. **Calculate the Number of Protons and Neutrons:**
- For Boron (B):
- Protons (p) = Atomic number = 5
- Neutrons (n) = Mass number - Atomic number = 10 - 5 = 5
- For Beryllium (Be):
- Protons (p) = Atomic number = 4
- Neutrons (n) = Mass number - Atomic number = 10 - 4 = 6
- For Nitrogen (N):
- Protons (p) = Atomic number = 7
- Neutrons (n) = Mass number - Atomic number = 14 - 7 = 7
- For Oxygen (O):
- Protons (p) = Atomic number = 8
- Neutrons (n) = Mass number - Atomic number = 16 - 8 = 8

3. **Calculate the n/p Ratio for Each Nucleus:**
- For Boron:
- n/p = 5/5 = 1
- For Beryllium:
- n/p = 6/4 = 1.5
- For Nitrogen:
- n/p = 7/7 = 1
- For Oxygen:
- n/p = 8/8 = 1

4. **Compare the n/p Ratios:**
- Boron: 1
- Beryllium: 1.5
- Nitrogen: 1
- Oxygen: 1

5. **Determine the Most Unstable Nucleus:**
- Among the calculated n/p ratios, Beryllium has the highest ratio of 1.5. Therefore, Beryllium is the most unstable nucleus among the options provided.

### Conclusion:
The unstable nucleus among the given options is **Beryllium (Be)**.

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