Question

what Percent of original radioactive substance is left after 5 half life time (A) \(3 \%\) (B) \(5 \%\) (C) \(6 \%\) (D) \(12 \%\)

Short answer

The remaining percentage of the original radioactive substance after 5 half-lives is approximately \(3\%\), so the correct answer is (A) \(3\%\).

Step-by-step solution

Understand the half-life formula

Half-life (t1/2) is the time it takes for the initial quantity of a radioactive substance to decrease by half. The formula for calculating the remaining quantity after n half-lives have passed is given by: Remaining quantity = Initial quantity * (1/2)^n Where n is the number of half-lives and (1/2)^n is the fraction of the radioactive substance remaining.

Apply the formula for the given number of half-lives

In this exercise, we are given that n = 5, which means that 5 half-lives have passed. We will now apply the formula to find the remaining percentage of the initial radioactive substance: Remaining percentage = (1/2)^5

Calculate the remaining percentage

To find the remaining percentage, raise 1/2 to the power of 5: Remaining percentage = (1/2)^5 = 1/32 = 0.03125 Now, to convert this fraction into a percentage, we multiply by 100: Remaining percentage = 0.03125 * 100 = 3.125% Since the given answer choices are all integers, we must round this value to the nearest integer. In this case, the closest integer value is 3%.

Find the answer

The remaining percentage of the original radioactive substance after 5 half-lives is approximately 3%, so the correct answer is: (A) 3%