JEE Main & Advanced Physics Nuclear Physics And Radioactivity Question Bank Topic Test - Nuclear Physics and Radioactivity

The half-life of a sample of a radioactive substance is 1 hour. If \[8\times {{10}^{10}}\] atoms are present at \[t=0\], then the number of atoms decayed in the duration \[t=2\] hour to \[t=4\] hour will be

A) \[2\times {{10}^{10}}\]

B) \[1.5\times {{10}^{10}}\]

C) Zero

D) Infinity

Correct Answer: B

Solution :

[b]\[N={{N}_{0}}{{\left( \frac{1}{2} \right)}^{\frac{t}{{{T}_{1l2}}}}}\]

No of atoms at t = 2hr, \[{{N}_{1}}=8\times {{10}^{10}}{{\left( \frac{1}{2} \right)}^{\frac{2}{1}}}=2\times {{10}^{10}}\]

No. of atoms at t = 4hr, \[{{N}_{2}}=8\times {{10}^{10}}{{\left( \frac{1}{2} \right)}^{\frac{4}{1}}}=\frac{1}{2}\times {{10}^{10}}\]

\[\therefore \] No. of atoms decayed in given duration

\[=\left( 2-\frac{1}{2} \right)\times {{10}^{10}}=1.5\times {{10}^{10}}\]