After `1 alpha` and `2 beta` emissions.

Options

A. Mass number reduces by `3`
B. Mass number reduces by `4`
C. Mass number reduces by `6`
D. Atomic number remains unchanged.

Explanation

To solve the problem of determining the new atomic number and mass number after one alpha and two beta emissions, we can follow these steps:

### Step 1: Understand the emissions
- **Alpha emission**: When an alpha particle (which consists of 2 protons and 2 neutrons) is emitted, the mass number decreases by 4, and the atomic number decreases by 2.
- **Beta emission**: When a beta particle (an electron) is emitted, a neutron is converted into a proton. This results in the atomic number increasing by 1, while the mass number remains unchanged.

### Step 2: Initial parameters
Let the initial mass number be \( A \) and the initial atomic number be \( Z \).

### Step 3: Apply alpha emission
After one alpha emission:
- New mass number \( A' = A - 4 \)
- New atomic number \( Z' = Z - 2 \)

### Step 4: Apply first beta emission
After the first beta emission:
- Mass number remains the same: \( A' = A - 4 \)
- New atomic number \( Z'' = Z' + 1 = (Z - 2) + 1 = Z - 1 \)

### Step 5: Apply second beta emission
After the second beta emission:
- Mass number remains the same: \( A' = A - 4 \)
- New atomic number \( Z''' = Z'' + 1 = (Z - 1) + 1 = Z \)

### Step 6: Final results
After one alpha and two beta emissions:
- Final mass number: \( A - 4 \)
- Final atomic number: \( Z \)

### Conclusion
The final result shows that the atomic number remains unchanged, while the mass number decreases by 4.