Question

The mean lives of a radioactive material for aand b radiations are 1620 years and 520 years respectively. The material decays simultaneously for a and b decay. The time after which one fourth of the material remains undecayed is-

• A. 540 years
• B. 324 years
• C. 720 years
• D. 840 years

Answer 1

Answer: (A)

540 years

Answer 2

t=$\frac { \tau _ { \alpha } \tau _ { \beta } } { \tau _ { \alpha } + \tau _ { \beta } }$= $\frac { 1620 \times 520 } { 1620 + 520 }$

= 394 years

t = time of decay = 2.303 log₁₀ × t

= 2.303 × log₁₀ 4 × 394 = 540 years