Radioactivity

The fraction of a radioactive element that decays over a given period of time is given by the formula: Where:
is the amount of the substance remaining after time ,
is the initial amount of the substance,
is the half-life of the substance.
The fraction that decays is given by:
Given:
,
. Substitute the values: Thus, the fraction that will decay in 30 years is 0.75.

The correct answer is (C) : 0.75.

Given:

• Half-life of the radioactive sample, years
• Final activity is of the initial activity

Decay Formula:

Substituting values:

Taking natural logarithm on both sides:

Using values:

Solving for :

Answer: The time required is 7 years (Option A).