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 solve the problem of finding 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 1: Understand the emission of an alpha particle
An alpha particle consists of 2 protons and 2 neutrons. When an atom emits an alpha particle, it loses these 4 nucleons (2 protons and 2 neutrons).

### Step 2: Determine the new atomic number and mass number
The original atom \( X \) has:
- Atomic number (Z) = 92
- Mass number (A) = 238

After emitting an alpha particle, the new atom (let's call it \( Y \)) will have:
- New atomic number \( Z' = Z - 2 = 92 - 2 = 90 \)
- New mass number \( A' = A - 4 = 238 - 4 = 234 \)

### Step 3: Write down the new atomic structure
The new atom \( Y \) has:
- Atomic number \( Z' = 90 \)
- Mass number \( A' = 234 \)

### Step 4: Calculate the number of neutrons
The number of neutrons (N) in an atom can be calculated using the formula:
\[ N = A' - Z' \]
Substituting the values we have:
\[ N = 234 - 90 = 144 \]

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