NEET Chemistry NEET PYQ-Nuclear Chemistry

The half-life of a radioactive isotope is three hours. If the initial mass of the isotope was 300 g, the mass which remained undecayed after 18 hours would be: [AIPMT 2000]

A) 4.68 g

B) 2.34 g

C) 1.17 g

D) 9.36 g

Correct Answer: A

Solution :

[a] Given

Half-life \[({{t}_{1/2}})=3\text{ }h\]

Initial mass \[({{N}_{0}})=300\,g\]

Total time \[(T)=18\text{ }h\]

Mass left \[(N)=?\]

We know that, \[\frac{N}{{{N}_{0}}}={{\left( \frac{1}{2} \right)}^{n}}\]

where n = number of half life

\[n=\frac{Total\,time}{Half-life}=\frac{18}{3}=6\]

So, \[\frac{N}{300}={{\left( \frac{1}{2} \right)}^{6}}\]

or \[\frac{N}{300}=\frac{1}{64}\]

\[N=\frac{300}{64}=4.68\,g\]