Half life of a radioactive material during radioactive decay is \(\underline{\hspace{1cm}}\).
Show Hint
- directly proportional to the initial concentration
- inversely proportional to the initial concentration and directly proportional to decay constant
- directly proportional to the final concentration and inversely proportional to decay constant
- independent of the initial concentration and inversely proportional to decay constant
The Correct Option is D
Solution and Explanation
Step 1: Define radioactive half-life (\(t_{1/2}\)).
The half-life is the time required for a quantity of a radioactive substance to be reduced to half of its initial value.
Step 2: State the formula relating half-life and the decay constant.
Radioactive decay is a first-order process. The relationship between the half-life and the decay constant (\(\lambda\)) is:
\[ t_{1/2} = \frac{\ln(2)}{\lambda} \]
Step 3: Analyze the relationship.
From the formula, we can see two things:
1. The half-life (\(t_{1/2}\)) is inversely proportional to the decay constant (\(\lambda\)).
2. The formula does not contain any terms for the initial or final concentration/amount of the substance. This means the half-life is independent of these quantities.
Conclusion: The half-life is independent of the initial concentration and inversely proportional to the decay constant.
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