After the emission of `alpha`-particle from the atom `X_92^238`, the number of neutrons in the atom will be

Options

A. 138
B. 140
C. 144
D. 150

Answer

To find the number of neutrons in the atom after the emission of an alpha particle from the atom \( X_{92}^{238} \), we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Alpha Particle**: An alpha particle is equivalent to \( ^4_2He \), which means it has a mass number of 4 and an atomic number of 2.

2. **Identify the Initial Atom**: The initial atom is \( X_{92}^{238} \). Here, the atomic number (Z) is 92 and the mass number (A) is 238.

3. **Write the Decay Equation**: When an alpha particle is emitted, the decay can be represented as:
\[ X_{92}^{238} \rightarrow Y_{Z}^{A} + ^4_2He \]
where \( Y \) is the new atom formed after the emission of the alpha particle.

4. **Calculate the New Atomic Number (Z)**:
- The new atomic number \( Z \) can be calculated as:
\[ Z = 92 - 2 = 90 \]
(since 2 protons are lost due to the emission of the alpha particle).

5. **Calculate the New Mass Number (A)**:
- The new mass number \( A \) can be calculated as:
\[ A = 238 - 4 = 234 \]
(since 4 nucleons are lost due to the emission of the alpha particle).

6. **Determine the Number of Protons and Neutrons**:
- The new atom formed is \( Y_{90}^{234} \).
- The number of protons in \( Y \) is 90 (from the atomic number).
- The mass number \( A \) is the sum of protons and neutrons:
\[ A = \text{Protons} + \text{Neutrons} \]
\[ 234 = 90 + \text{Neutrons} \]

7. **Calculate the Number of Neutrons**:
- Rearranging the equation gives:
\[ \text{Neutrons} = 234 - 90 = 144 \]

### Final Answer:
The number of neutrons in the atom after the emission of the alpha particle is **144**.

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