Half-life period for radioactive element is

Options

A. Always constant
B. Variable
C. Independent of final concentrationn
D. Independent of initial concentration

Explanation

To solve the question regarding the half-life period of a radioactive element, we will break down the explanation into clear steps.

### Step-by-Step Solution:

1. **Understanding Half-Life**:
- The half-life (t₁/₂) of a radioactive element is defined as the time required for the quantity of the radioactive substance to reduce to half of its initial amount.
- Mathematically, if the initial concentration is C₀, then after one half-life, the concentration will be C₀/2.

2. **Independence of Concentration**:
- The half-life period is independent of both the initial concentration and the final concentration of the radioactive element. This means that regardless of how much of the substance you start with, the time it takes to decay to half remains constant.

3. **Relationship with Decay Constant**:
- The half-life is related to the decay constant (k) by the formula:
\[ t_{1/2} = \frac{0.693}{k} \]
- Here, 0.693 is the natural logarithm of 2, which is a constant. The decay constant (k) is also a characteristic of the radioactive substance and remains constant for a given isotope.

4. **Conclusion**:
- Since both 0.693 and k are constants, the half-life (t₁/₂) is also a constant value. It does not change with varying concentrations of the radioactive substance.

5. **Correct Options**:
- Based on the explanation, the correct options regarding the half-life period of a radioactive element are that it is constant and independent of initial and final concentrations. Therefore, options A, B, and D are correct, while option C is incorrect.