Question

10 g of a radioactive element loses 8.75 g in 9 days. Thus, the half-life is x days.Find out the value of x:

• A. x=2
• B. x=3
• C. x=5
• D. None of these

Answer 1

Answer: (B)

x=3

we will use the formula for half life of 1st order reaction
1)$\left[A\right]=\frac{1}{2}[A{]}_o$
2)$t_{1/2}=\ln 2k\approx 0.693k$
we get,
3).$k=-\frac{\ln \frac{[A{]}_t}{[A{]}_o}}{t}=-\frac{\ln \frac{0.375g}{3g}}{36\text{min}}=0.0578{\text{min}}^{-1}$
$k=-\frac{\ln \frac{[A{]}_t}{[A{]}_o}}{t}=-\frac{\ln \frac{1.25g}{10g}}{9days}=0.231{day}^{-1}$
using 2) and 3)
$t_{1/2}=\ln 2k\approx \frac{0.693}{0.231{days}^{-1}}\approx 3days$
Ans-3