Question

The half-life period of a radioactive element is 150 days. After 600 days, 1 gm of the element will be reduced to:

• A. \( \frac{1}{32} \, \text{gm} \)
• B. \( \frac{15}{16} \, \text{gm} \)
• C. \( \frac{1}{8} \, \text{gm} \)
• D. \( \frac{1}{16} \, \text{gm} \)

Hint:

Use the half-life formula to calculate the remaining quantity of a radioactive element after a given number of half-lives.

Answer 1

The Correct Option is D

The half-life equation is given by: \[ N = N_0 \times \left( \frac{1}{2} \right)^{\frac{t}{T}} \] Where: - \( N_0 = 1 \, \text{gm} \) (initial mass) - \( t = 600 \, \text{days} \) - \( T = 150 \, \text{days} \) (half-life) Substitute the values: \[ N = 1 \times \left( \frac{1}{2} \right)^{\frac{600}{150}} = 1 \times \left( \frac{1}{2} \right)^4 = \frac{1}{16} \] Thus, after 600 days, the remaining mass is \( \frac{1}{16} \, \text{gm} \).