Question

A nucleus of $Ux_{1}$ has a half life of $24.1$ days how long a sample of $Ux_{1}$will take to change to 90% of $Ux_{1}$

• A. 80 days
• B. 40 days
• C. 20 days
• D. 10 days

Answer 1

Answer: (A)

80 days

Answer 2

: Here, $\lambda = \frac{0.693}{T_{1/2}} = \frac{0.693}{24.1} = 0.02876day^{- 1}$

$N = N_{0} - 90\% ofN_{0} = \frac{N_{0}}{10}$

As $N = N_{0}e^{- \lambda t}$

$\therefore\frac{N_{0}}{10} = N_{0}e^{- \lambda t}or\frac{1}{10} = e^{- \lambda t}or1 = e^{\lambda t}$

Or $\log_{e}{}10 = \lambda t$

$\therefore t = \frac{1}{\lambda}\log_{e}{}10 = \frac{2.303\log 10}{0.02870} = \frac{2.303 \times 1}{0.02876} = 80days$