Number of neutrons i8n a parent nucleus `X`, which gives `._(7)^(14)N` after two sucessive `beta-` emission would be:

Options

A. 9
B. 6
C. 7
D. 8

Explanation

To find the number of neutrons in the parent nucleus \( X \) that transforms into \( _{7}^{14}N \) after two successive beta emissions, we can follow these steps:

### Step 1: Understand Beta Emission
In beta emission, a neutron in the nucleus is transformed into a proton while emitting a beta particle (an electron). This process increases the atomic number by 1 but does not change the mass number.

### Step 2: Determine the Atomic Number and Mass Number of Nitrogen
From the given information, we know that after two beta emissions, the nucleus becomes \( _{7}^{14}N \):
- Atomic number (Z) = 7
- Mass number (A) = 14

### Step 3: Determine the Atomic Number of the Parent Nucleus
Since each beta emission increases the atomic number by 1, we can deduce the atomic number of the parent nucleus \( X \):
- After 1 beta emission: Atomic number = 7 - 1 = 6
- After 2 beta emissions: Atomic number = 6 - 1 = 5

Thus, the atomic number of the parent nucleus \( X \) is 5.

### Step 4: Calculate the Mass Number of the Parent Nucleus
The mass number remains unchanged during beta decay. Therefore, the mass number of the parent nucleus \( X \) is the same as that of the final nucleus:
- Mass number of \( X \) = 14

### Step 5: Calculate the Number of Neutrons in the Parent Nucleus
The number of neutrons can be calculated using the formula:
\[ \text{Number of Neutrons} = \text{Mass Number} - \text{Atomic Number} \]
Substituting the values we have:
\[ \text{Number of Neutrons} = 14 - 5 = 9 \]

### Conclusion
The number of neutrons in the parent nucleus \( X \) is 9.

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