Question

A radioactive element having half-life (30 min) is undergoing beta decay. The fraction of radioactive element remains undecayed after (90 min) will be

• A. (\frac{1}{2})
• B. (\frac{1}{4})
• C. (\frac{1}{8})
• D. [suspicious link removed]

Hint:

Remaining quantity $N = N_0(1/2)^n$, where $n$ is the number of elapsed half-lives.

Answer 1

The Correct Option is C

Step 1: Number of Half-lives
$n = \frac{\text{Total Time}}{\text{Half-life}} = \frac{90 \text{ min}}{30 \text{ min}} = 3$.

Step 2: Remaining Fraction
Fraction remaining $= (\frac{1}{2})^n = (\frac{1}{2})^3$.

Step 3: Calculation
Fraction $= \frac{1}{8}$.
Final Answer: (C)