If `U_92^236` nucleus emits one `alpha`-particle, the remaining nucleus will have

Options

A. 119 neutrons and 119 protons
B. 142 neutrons and 90 protons
C. 144 neutrons and 92 protons
D. 146 neutrons and 90 protons

Answer

To solve the problem of what the remaining nucleus will be after a uranium-236 nucleus emits one alpha particle, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Initial Nucleus**:
The initial nucleus is uranium-236, denoted as \( _{92}^{236}U \).

2. **Understand Alpha Particle Emission**:
An alpha particle is essentially a helium nucleus, which has a mass number of 4 and an atomic number of 2. When an alpha particle is emitted, the remaining nucleus will lose both mass and atomic numbers.

3. **Apply Conservation of Mass Number**:
The mass number before emission must equal the mass number after emission.
\[ A_{initial} = A_{final} + A_{alpha} \]
Here, \( A_{initial} = 236 \) and \( A_{alpha} = 4 \). Therefore:
\[ 236 = A_{final} + 4 \]
Solving for \( A_{final} \):
\[ A_{final} = 236 - 4 = 232 \]

4. **Apply Conservation of Atomic Number**:
Similarly, the atomic number must also be conserved:
\[ Z_{initial} = Z_{final} + Z_{alpha} \]
Here, \( Z_{initial} = 92 \) and \( Z_{alpha} = 2 \). Therefore:
\[ 92 = Z_{final} + 2 \]
Solving for \( Z_{final} \):
\[ Z_{final} = 92 - 2 = 90 \]

5. **Determine the Remaining Nucleus**:
After the emission of one alpha particle, the remaining nucleus is \( _{90}^{232}X \), where \( X \) represents the new element.

6. **Calculate Number of Protons and Neutrons**:
- The number of protons is equal to the atomic number, which is 90.
- The number of neutrons can be calculated using the formula:
\[ N = A - Z \]
Where \( N \) is the number of neutrons, \( A \) is the mass number, and \( Z \) is the atomic number.
\[ N = 232 - 90 = 142 \]

### Final Result:
The remaining nucleus after the emission of one alpha particle from uranium-236 is \( _{90}^{232}X \), which has 90 protons and 142 neutrons.