Question

A radioactive sample has half-life of \(5\) years. The percentage of fraction decayed in \(10\) years will be

• A. \(25\%\)
• B. \(50\%\)
• C. \(75\%\)
• D. \(90\%\)

Hint:

After n half-lives the remaining fraction is (1/2)^n.

Answer 1

The Correct Option is C

Step 1: Number of Half-Lives:
\(n=\dfrac{10}{5}=2\).

Step 2: Remaining Fraction:
\(\dfrac N{N_0}=\left(\dfrac12\right)^2=\dfrac14=25\%\).

Step 3: Decayed Fraction:
Decayed \(=100\%-25\%=75\%\).

Step 4: Check the Other Options:
25% is the remaining amount, not the decayed one. 50% is the decay after one half-life. 90% would need more than three half-lives.

Final Answer:
75% of the sample has decayed, option (C). \[ \boxed{\text{(C) } 75\%} \]