Two identical nuclei A and B of the same radioactive element undergo `beta` decay. A emits a `beta`-particle and changes to A'. B emits a `beta`-particle and then a `gamma`-photon immediately afterwards, and changes to B'

Options

A. A. and B. have the same atomic number and mass number
B. A and B. have the same atomic number and different mass numbers
C. A. and B. have different atomic numbers but the same mass number
D. A and B are isotopes

Answer

To solve the problem, we need to analyze the decay processes of nuclei A and B step by step.

### Step 1: Understanding Beta Decay
In beta decay, a nucleus emits a beta particle (which is an electron or positron). This process results in an increase in the atomic number (Z) of the nucleus by 1, while the mass number (A) remains unchanged.

- **For nucleus A**:
- Initial atomic number: Z
- After beta decay: Atomic number becomes Z + 1
- Mass number remains A

Thus, nucleus A transforms into A' with:
- Atomic number: Z + 1
- Mass number: A

### Step 2: Understanding Gamma Decay
Gamma decay occurs when a nucleus transitions from a higher energy state to a lower energy state, emitting a gamma photon. This process does not change the atomic number or mass number of the nucleus.

- **For nucleus B**:
- Initially, it undergoes beta decay, so:
- Atomic number becomes Z + 1
- Mass number remains A
- Then, it emits a gamma photon, which has no effect on the atomic number or mass number.

Thus, nucleus B transforms into B' with:
- Atomic number: Z + 1
- Mass number: A

### Step 3: Comparing Nuclei A' and B'
After both decay processes, we have:
- Nucleus A' with:
- Atomic number: Z + 1
- Mass number: A
- Nucleus B' with:
- Atomic number: Z + 1
- Mass number: A

### Conclusion
Since both A' and B' have the same atomic number (Z + 1) and the same mass number (A), we can conclude that:
- A and B have the same atomic number and mass number.

Therefore, the correct answer is:
**A and B have the same atomic number and mass number.**

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