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  4. The half-life of radium is 1600 years. The time does 1g of radium take to reduce to 0.125g is

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Q. The half-life of radium is 1600 years. The time does 1g of radium take to reduce to 0.125g is

NTA AbhyasNTA Abhyas 2022

Solution:

Nuclear reactions are Ist order reaction
$\frac{N}{N_{0}}=\left(\frac{1}{2}\right)^{n}$
$\Rightarrow \frac{0.125}{1}=\left(\right. \frac{1}{2} \left.\right)^{n}$
$=\frac{1}{8}=\frac{1}{2^{n}}$
$\Rightarrow n=3$
$n=\frac{t}{t_{\frac{1}{2}}}$ ;
$\because \, \, 3=\frac{t}{1600}$
$t=4800$