What happens to the (i) atomic number, (ii) mass number of the nucleus of an element when (a) an `alpha`-particle, (b) a `beta`-particle, and ( c) `gamma` radiation, is emitted ?

Answer

To solve the question regarding the changes in atomic number and mass number when different types of radiation are emitted from a nucleus, we will analyze each case step by step.

### Step-by-Step Solution:

1. **Emission of an Alpha Particle:**
- When an alpha particle (which consists of 2 protons and 2 neutrons) is emitted from a nucleus:
- **Atomic Number (Z):** Decreases by 2.
- **Mass Number (A):** Decreases by 4.
- Therefore, if the original nucleus has an atomic number Z and mass number A, after the emission of an alpha particle, the new nucleus will have:
- Atomic Number: \( Z - 2 \)
- Mass Number: \( A - 4 \)

2. **Emission of a Beta Particle:**
- When a beta particle (which is an electron) is emitted from a nucleus:
- **Atomic Number (Z):** Increases by 1.
- **Mass Number (A):** Remains unchanged.
- Thus, if the original nucleus has an atomic number Z and mass number A, after the emission of a beta particle, the new nucleus will have:
- Atomic Number: \( Z + 1 \)
- Mass Number: \( A \)

3. **Emission of Gamma Radiation:**
- When gamma radiation (which is a form of electromagnetic radiation) is emitted:
- **Atomic Number (Z):** Remains unchanged.
- **Mass Number (A):** Remains unchanged.
- Therefore, if the original nucleus has an atomic number Z and mass number A, after the emission of gamma radiation, the new nucleus will have:
- Atomic Number: \( Z \)
- Mass Number: \( A \)

### Summary of Changes:
- **Alpha Particle Emission:**
- Atomic Number: \( Z - 2 \)
- Mass Number: \( A - 4 \)

- **Beta Particle Emission:**
- Atomic Number: \( Z + 1 \)
- Mass Number: \( A \)

- **Gamma Radiation Emission:**
- Atomic Number: \( Z \)
- Mass Number: \( A \)