Question

The half life of a radioactive element is $10$ days. If the mass of the specimen reduces to $(1/10{)}^{th}$ then the time taken is :-

• A. $100$ days
• B. $50$ days
• C. $33$ days
• D. $16$ days

Answer 1

Answer: (C)

$33$ days

The remaining amount after decay is given as,

$N=N_0{e}^{-\frac{0.693t}{t_{1/2}}}$

$\frac{N_0}{10}=N_0{e}^{-\frac{0.693t}{10}}$

$\ln 10=\frac{0.693t}{10}$

$t\approx 33days$