`._6^12 C` absorbs an energenic neutron and emits beta particles. The resulting nucleus is.

Options

A. `._7^14 N`
B. `._7^13 N`
C. `._5^13 B`
D. `._6^13 C`

Explanation

To solve the problem, we need to analyze the nuclear reaction involving the carbon isotope \( _6^{12}C \) when it absorbs a neutron and emits a beta particle.

### Step-by-Step Solution:

1. **Identify the Initial Nucleus**:
The initial nucleus is \( _6^{12}C \). Here, 6 is the atomic number (number of protons) and 12 is the mass number (total number of protons and neutrons).

2. **Absorption of a Neutron**:
When \( _6^{12}C \) absorbs a neutron, we can represent the neutron as \( _0^{1}n \). The reaction can be written as:
\[ _6^{12}C + _0^{1}n \rightarrow ? \]

3. **Calculate the New Mass Number**:
The mass number increases by 1 due to the addition of the neutron:
\[ 12 + 1 = 13 \]
So, the new mass number will be 13.

4. **Emitting a Beta Particle**:
A beta particle is represented as \( _{-1}^{0}e \) (or \( \beta^- \)). When a beta particle is emitted, a neutron in the nucleus is converted into a proton. This results in:
- The atomic number increases by 1 (since a neutron is converted to a proton).
- The mass number remains the same (since we are just changing a neutron to a proton).

5. **Calculate the New Atomic Number**:
The new atomic number after the emission of the beta particle will be:
\[ 6 + 1 = 7 \]

6. **Write the Resulting Nucleus**:
After these changes, the resulting nucleus can be represented as:
\[ _7^{13}N \]
This indicates that we have a nitrogen nucleus with 7 protons and 6 neutrons.

### Final Answer:
The resulting nucleus after \( _6^{12}C \) absorbs a neutron and emits a beta particle is \( _7^{13}N \).