Select the correct statement(s)

Options

A. Mass number remains constant when positron emission takes place
B. One neutron converts into proton in `beta(._(-1)^(0)e)` emission process
C. Activity of a radioactive substance double when temp. increases from 300 K to 310 K
D. Isodiaphers formed when one alpha particle emitted and isotopes formed when 2 beta particles emitted

Answer

To solve the question "Select the correct statement(s)", we will evaluate each statement one by one based on our understanding of nuclear chemistry, particularly focusing on positron emission, beta emission, and the effects of temperature on radioactive decay.

### Step-by-Step Solution:

1. **Evaluate the First Statement**:
- **Statement**: "Mass number remains constant when positron emission takes place."
- **Analysis**: In positron emission, a proton in the nucleus is converted into a neutron and a positron is emitted. The mass number (total number of protons and neutrons) does not change because one proton is lost and one neutron is gained. Therefore, this statement is **correct**.

2. **Evaluate the Second Statement**:
- **Statement**: "One neutron is converted into a proton in the beta emission process."
- **Analysis**: In beta emission, a neutron is indeed converted into a proton, and a beta particle (electron) is emitted. This means the atomic number increases by 1 while the mass number remains the same. Hence, this statement is also **correct**.

3. **Evaluate the Third Statement**:
- **Statement**: "Activity of a radioactive substance doubles when temperature increases from 300 to 310 K."
- **Analysis**: The activity of a radioactive substance is given by the equation \( A = \lambda N \), where \( \lambda \) is the decay constant and \( N \) is the number of radioactive nuclei. The decay constant \( \lambda \) does not depend on temperature, and thus the activity does not double with a temperature increase. Therefore, this statement is **incorrect**.

4. **Evaluate the Fourth Statement**:
- **Statement**: "Isodiaphore formed when one alpha particle is emitted and isotope formed when two beta particles are emitted."
- **Analysis**: Isodiaphors are nuclides that have the same number of nucleons (mass number) but different atomic numbers. When an alpha particle is emitted, the mass number decreases by 4 and the atomic number decreases by 2, which does not form isodiaphors. When two beta particles are emitted, the mass number remains the same, but the atomic number increases by 2, leading to the formation of isotopes. Thus, this statement is **incorrect**.

### Summary of Statements:
- **First Statement**: Correct
- **Second Statement**: Correct
- **Third Statement**: Incorrect
- **Fourth Statement**: Incorrect

### Final Answer:
The correct statements are the **first and second statements**.