Question

2 g of a radioactive sample having half-life of 15 days was synthesised on 1st Jan 2009. The amount of the sample left behind on 1st March, 2009 (including both the days) is

• A. 0 g
• B. 0.125 g
• C. 1 g
• D. 0.5 g

Hint:

Amount left = Initial amount / $2^n$, where $n$ is the number of half-lives.

Answer 1

The Correct Option is B

Step 1: Calculate Total Time
From January 1st to March 1st, 2009, the total time elapsed is 60 days.
Step 2: Find Number of Half-lives
Half-life ($t_{1/2}$) is 15 days. Number of half-lives ($n$) = $60 / 15 = 4$.
Step 3: Calculate Remaining Amount
Using the formula $N = N_{0}(1/2)^{n}$, where $N_{0} = 2~g$. $N = 2 \times (1/2)^{4} = 2 \times 1/16 = 0.125~g$.
Final Answer: (b)