Question

If 96.875% of a radioactive substance decays in 10 days, then the half life of the substance is (in days)

• A. 10
• B. 5
• C. 4
• D. 2

Hint:

Memorize powers of 2: \( 2^5 = 32 \). Also, \( 3.125% \) is a common fraction in radioactive decay problems corresponding to \( 1/32 \).

Answer 1

The Correct Option is D

Step 1: Understanding the Concept:

We need to find the number of half-lives passed for the substance to decay by a certain percentage. Remaining amount \( N = N_0 \times (1/2)^n \), where \( n \) is the number of half-lives.
Step 2: Key Formula or Approach:

\( \text{Fraction Remaining} = \frac{100 - \text{Decayed %}}{100} \) \( n = \frac{\text{Total Time}}{\text{Half Life}} \)
Step 3: Detailed Explanation:

Percentage Decayed = 96.875% Percentage Remaining = \( 100 - 96.875 = 3.125% \) Fraction Remaining = \( \frac{3.125}{100} = \frac{1}{32} \). We know that \( \frac{1}{32} = \left(\frac{1}{2}\right)^5 \). So, 5 half-lives have passed (\( n = 5 \)). Total time given = 10 days. \( n \times T_{1/2} = 10 \) \( 5 \times T_{1/2} = 10 \) \( T_{1/2} = 2 \) days.
Step 4: Final Answer:

The half life is 2 days.