Question

The half-life period of radium is 1600 yr. The fraction of a sample of radium that would remain after 6400 yr is

• A. \(\dfrac{1}{4}\)
• B. \(\dfrac{1}{2}\)
• C. \(\dfrac{1}{8}\)
• D. \(\dfrac{1}{16}\)

Hint:

After \(n\) half-lives: \(N = N_0 \left(\dfrac{1}{2}\right)^n\). Always calculate \(n = t/T_{1/2}\) first.

Answer 1

The Correct Option is D

Step 1: Understanding the Concept:
After \(n\) half-lives, fraction remaining \(= \left(\dfrac{1}{2}\right)^n\).
Step 2: Detailed Explanation:
Number of half-lives \(= \dfrac{6400}{1600} = 4\)
Fraction remaining \(= \left(\dfrac{1}{2}\right)^4 = \dfrac{1}{16}\)
Step 3: Final Answer:
Fraction remaining \(= \mathbf{\dfrac{1}{16}}\).