# NEET Physics Nuclei Questions Solved

NEET - 2011

Two radioactive nuclei P and Q, in a given sample decay into a stable nucleous R. At time t=0, number of P species are $4{N}_{0}$ and that of Q are ${N}_{0}$ and that of Q are ${N}_{0}.$Half -life of P(for conversion to R) is 1 min where as that of Q is 2 min. Initially there are no nuclei of R present in the sample. When number of nuclei of P and Q are equal, the number of nuclei of R present in the sample would be

(a)$3{N}_{0}$                                          (b)$\frac{9{N}_{0}}{2}$

(c)$\frac{5{N}_{0}}{2}$                                       (d)$2{N}_{0}$

Initially $P\to 4{N}_{0}$

$Q\to {N}_{0}$

Half life

${T}_{Q}\to 2min$

Let after time t number of nuclei of P and Q are equal i.e,$\frac{4{N}_{0}}{{2}^{1/1}}=\frac{{N}_{0}}{{2}^{1/2}}$

$4={2}^{1/2}$

${2}^{2}={2}^{1/2}$

$\frac{t}{2}=2$

t=4min

Disactive nucleus or Nuclei of R

$=\left(4{N}_{0}-\frac{4{N}_{0}}{{2}^{4}}\right)+\left({N}_{0}-\frac{{N}_{0}}{{2}^{2}}\right)$

$=4{N}_{0}-\frac{{N}_{0}}{4}+{N}_{0}-\frac{{N}_{0}}{4}$

$=5{N}_{0}-\frac{{N}_{0}}{2}$$=\frac{9}{2}{N}_{0}$

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