NEET Physics Nuclear Physics And Radioactivity NEET PYQ-Nuclear Physics

Half-life of a radioactive substance is 12.5 h and its mass is 256 g. After what time, the amount of remaining substance is 1g?                                                                                                          [AIPMT 2001]

A) 75 h

B) 100 h

C) 125 h

D)      150 h

Correct Answer: B

Solution :

The mass of radioactive substance remained is,

\[M={{M}_{0}}{{\left( \frac{1}{2} \right)}^{n}}\]

Here, \[M=1\,g,\,\,{{M}_{0}}=256\,g,\,{{t}_{1/2}}=12.5\,h\]

So, \[1=256\,{{\left( \frac{1}{2} \right)}^{n}}\]

or \[\frac{1}{256}={{\left( \frac{1}{2} \right)}^{n}}\]

or \[{{\left( \frac{1}{2} \right)}^{8}}={{\left( \frac{1}{2} \right)}^{N}}\]

Comparing the powers on both the sides, we get

\[n=8=\frac{t}{{{T}_{1/2}}}\]

\[\therefore \] \[t=8{{T}_{1/2}}=8\times 12.5=100\,h\]