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 find the number of neutrons in the parent nucleus that emits \( N^{14} \) through beta emission, we can follow these steps:

### Step 1: Identify the daughter nucleus
The daughter nucleus formed after beta emission is \( N^{14} \) (Nitrogen-14). The atomic number of nitrogen (N) is 7.

### Step 2: Write the beta emission equation
In beta emission, a neutron in the parent nucleus is converted into a proton, and a beta particle (an electron) is emitted. The general equation can be written as:
\[ \text{Parent nucleus} \rightarrow \text{Daughter nucleus} + \beta^- \]
Let’s denote the parent nucleus as \( X \) with atomic number \( A \) and mass number \( Z \).

### Step 3: Determine the atomic number of the parent nucleus
Since the daughter nucleus \( N^{14} \) has an atomic number of 7, and one neutron is converted into a proton during beta decay, the atomic number of the parent nucleus \( X \) can be calculated as:
\[ A = 7 - 1 = 6 \]
Thus, the parent nucleus has an atomic number of 6, which corresponds to Carbon (C).

### Step 4: Determine the mass number of the parent nucleus
The mass number of the daughter nucleus \( N^{14} \) is 14. Since the mass number remains the same during beta decay, we can write:
\[ Z = 14 \]
This means the parent nucleus also has a mass number of 14.

### Step 5: Identify the parent nucleus
Now we can identify the parent nucleus:
\[ \text{Parent nucleus} = C^{14} \quad \text{(Carbon-14)} \]

### Step 6: Calculate the number of neutrons in the parent nucleus
The number of neutrons \( N \) in a nucleus can be calculated using the formula:
\[ N = Z - A \]
Where \( Z \) is the mass number and \( A \) is the atomic number. For Carbon-14:
\[ N = 14 - 6 = 8 \]

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

### Summary
- Parent nucleus: \( C^{14} \)
- Number of neutrons: **8**

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