Nuclear Physics

Step 1: Define radioactive half-life ( ).
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 ( ) is:

Step 3: Analyze the relationship.
From the formula, we can see two things: 1. The half-life ( ) is inversely proportional to the decay constant ( ). 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.