Assertion `(A):` Half life of a radioactive isotope is the time required to decrease its mass number by half.
Reason `(R) : ` Halt`-` of readioactive isotopes is independent of the initial amount of the isotope.

Options

A. If both `(A)` and `(R)` are correct , and `(R)` is the correct explanation of `(A)`
B. If both `(A)` and `(R)` are correct, but (R) is not the correct explanation of `(A)`
C. If `(A)` is correct, but `(R)` is incorrect.
D. If both `(A)` and `(R)` are incorrect.

Explanation

To solve the given question, we need to analyze both the assertion and the reason provided.

### Step 1: Understand the Assertion
The assertion states: "Half-life of a radioactive isotope is the time required to decrease its mass number by half."

- **Analysis**: The half-life (T½) refers to the time it takes for half of the radioactive substance to decay, not specifically its mass number. The mass number is the total number of protons and neutrons in the nucleus of an atom, and it does not necessarily decrease by half in the same time frame. Therefore, this assertion is incorrect.

### Step 2: Understand the Reason
The reason states: "Half-life of radioactive isotopes is independent of the initial amount of the isotope."

- **Analysis**: This statement is true. The half-life of a radioactive isotope is a constant that does not depend on the initial quantity of the substance. It is a characteristic property of the isotope and is determined by its decay constant (k).

### Step 3: Conclusion
Now, we can conclude the relationship between the assertion and the reason:

- The assertion is **incorrect** because it misrepresents the concept of half-life in terms of mass number.
- The reason is **correct** as it accurately describes the independence of half-life from the initial amount of the isotope.

### Final Answer
- Assertion (A) is incorrect.
- Reason (R) is correct.