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  • A nucleus of   has a half life of 24.1 days. How long a sample of   will take to ch

A nucleus of  U x_1 has a half life of 24.1 days. How long a sample of  U x_1 will take to change to 90%  of  U x_1:

Option: 1

80 days


Option: 2

40 days 


Option: 3

20 days 


Option: 4

10 days


Answers (1)

best_answer

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

\mathrm{N}=\mathrm{N}_0-90 \% \text { of } \mathrm{N}_0=\frac{\mathrm{N}_0}{10}

\text { As } \mathrm{N}=\mathrm{N}_0 \mathrm{e}^{-\lambda \mathrm{t}}

\therefore \frac{\mathrm{N}_0}{10}=\mathrm{N}_0 \mathrm{e}^{-\lambda \mathrm{t}} \quad \text { or } \quad \frac{1}{10}=\mathrm{e}^{-\lambda \mathrm{t}} \quad \text { or } \quad 10=\mathrm{e}^{\lambda \mathrm{t}} \quad \text { or } \quad \log _{\mathrm{e}} 10=\lambda \mathrm{t}

\therefore \quad \mathrm{t}=\frac{1}{\lambda} \log _{\mathrm{e}} 10=\frac{2.303 \log 10}{0.02870}=\frac{2.303 \times 1}{0.02876}=80 \text { days }

Posted by

himanshu.meshram

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