After the emission of one `alpha`- particle followed by two `beta`-particles from `"" _(92) ^(238) U,` the number of neutrons in the newly formed nucleus is

Options

A. 140
B. 142
C. 144
D. 146

Explanation

To solve the problem, we need to determine the number of neutrons in the newly formed nucleus after the emission of one alpha particle and two beta particles from Uranium-238 (U-238).

### Step-by-Step Solution:

1. **Identify the Parent Nucleus:**
The parent nucleus is Uranium-238, which has an atomic number (Z) of 92 and a mass number (A) of 238.
\[ \text{Uranium-238: } \, ^{238}_{92}U \]

2. **Understand the Emissions:**
- **Alpha Particle Emission:** An alpha particle (α) consists of 2 protons and 2 neutrons. When an alpha particle is emitted, the atomic number decreases by 2 and the mass number decreases by 4.
- **Beta Particle Emission:** A beta particle (β) is an electron, which has negligible mass and a charge of -1. When a beta particle is emitted, the atomic number increases by 1, but the mass number remains unchanged.

3. **Calculate the Changes After Emission:**
- **After Emitting One Alpha Particle:**
- New atomic number: \( Z = 92 - 2 = 90 \)
- New mass number: \( A = 238 - 4 = 234 \)
- The new nucleus after alpha emission is:
\[ ^{234}_{90}X \]

- **After Emitting Two Beta Particles:**
- Each beta emission increases the atomic number by 1. Therefore, after two beta emissions:
- New atomic number: \( Z = 90 + 2 = 92 \)
- Mass number remains the same: \( A = 234 \)
- The final nucleus after both emissions is:
\[ ^{234}_{92}Y \]

4. **Determine the Number of Neutrons:**
The number of neutrons (N) in a nucleus can be calculated using the formula:
\[ N = A - Z \]
For the newly formed nucleus:
\[ N = 234 - 92 = 142 \]

5. **Final Answer:**
The number of neutrons in the newly formed nucleus is **142**.