The number of neutrons in the parent nucleus which gives `N^14` on `beta`-emission and the parent nucleus is

Options

A. `8, C^14`
B. `6,C^12`
C. `4, C^13`
D. None of these

Answer

To solve the problem of finding the number of neutrons in the parent nucleus that gives \( N^{14} \) on beta emission, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Product Nucleus**:
The product of the beta emission is \( N^{14} \) (Nitrogen-14). We know that Nitrogen has an atomic number of 7.

2. **Understand Beta Emission**:
In beta emission, a neutron in the nucleus is converted into a proton, and a beta particle (electron) is emitted. This process increases the atomic number by 1 while the mass number remains unchanged.

3. **Set Up the Parent Nucleus**:
Let the parent nucleus be represented as \( X \) with mass number \( A \) and atomic number \( Z \). The reaction can be represented as:
\[ X \rightarrow N^{14} + \beta^- \]
where \( N^{14} \) has \( A = 14 \) and \( Z = 7 \).

4. **Conserve Mass Number**:
The mass number before and after the reaction must be equal. Therefore:
\[ A = 14 + 0 \implies A = 14 \]

5. **Conserve Atomic Number**:
The atomic number before and after the reaction must also be equal. Therefore:
\[ Z + 1 = 7 \implies Z = 6 \]

6. **Identify the Parent Nucleus**:
The parent nucleus \( X \) has a mass number of 14 and an atomic number of 6, which corresponds to Carbon-14 (\( C^{14} \)).

7. **Calculate the Number of Neutrons**:
The number of neutrons \( n \) in the nucleus can be calculated using the formula:
\[ n = A - Z \]
Substituting the values we found:
\[ n = 14 - 6 = 8 \]

### Final Answer:
The number of neutrons in the parent nucleus \( C^{14} \) is **8**.