The number of beta particles emitter by radioactive sustance is twice the number of alpha particles emitter by it. The resulting daughter is an

Options

A. isomer of parent
B. isotone of parent
C. isotope of parent
D. isobar of parent

Explanation

To solve the problem, we need to analyze the emissions of alpha and beta particles from a radioactive substance and determine the nature of the resulting daughter nucleus.

### Step-by-Step Solution:

1. **Define the Parent Nucleus**:
Let the parent nucleus be represented as \( X \) with mass number \( A \) and atomic number \( Z \).

2. **Identify Particle Emissions**:
According to the problem, the number of beta particles emitted is twice the number of alpha particles emitted.
- Let the number of alpha particles emitted be \( n \).
- Then, the number of beta particles emitted will be \( 2n \).

3. **Determine Changes in Mass and Atomic Numbers**:
- Each alpha particle emission decreases the mass number by 4 and the atomic number by 2.
- Each beta particle emission does not change the mass number but increases the atomic number by 1 (since a beta particle is an electron emitted from the nucleus).

4. **Calculate the Resulting Daughter Nucleus**:
After emitting \( n \) alpha particles and \( 2n \) beta particles:
- The new mass number \( A' \) will be:
\[ A' = A - 4n \]
- The new atomic number \( Z' \) will be:
\[ Z' = Z - 2n + 2n = Z \]

5. **Analyze the Resulting Daughter Nucleus**:
- The atomic number \( Z' \) is equal to the original atomic number \( Z \), which means the daughter nucleus has the same atomic number as the parent nucleus.
- Since the mass number has changed (decreased by \( 4n \)), the daughter nucleus is not an isobar (which would have the same mass number).
- The daughter nucleus is also not an isomer, as isomers have the same mass and atomic numbers but different energy states.

6. **Conclusion**:
Since the atomic number remains the same and the mass number has decreased, the resulting daughter nucleus is an **isotope** of the parent nucleus.

### Final Answer:
The resulting daughter is an **isotope** of the parent nucleus.