Question

Half life of a radioactive material during radioactive decay is \(\underline{\hspace{1cm}}\).

• A. directly proportional to the initial concentration
• B. inversely proportional to the initial concentration and directly proportional to decay constant
• C. directly proportional to the final concentration and inversely proportional to decay constant
• D. independent of the initial concentration and inversely proportional to decay constant

Hint:

A key feature of first-order kinetics (which includes radioactive decay) is that the half-life is constant. It doesn't matter if you start with 1 kg or 1 gram of a substance; the time it takes for half of it to decay is always the same.

Answer 1

The Correct Option is D

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.