Question 544: Atoms & Nuclei

Question

Two radioactive nuclei P and Q, in a given sample decay into a stable nucleus R. At time t = 0. number of P species are 4 N
0
and that of Q are N
0
. Half -life of P (for conversion to R) is 1 minute where as that of Q is 2 minutes. 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

Accepted Answer

Initially P = 4N
0
Q = N
0
Half life T
P
= 1 min.
T
Q
= 2 min.
Let after time t number of nuclei of P and Q are
equal, that is
N
P
= N
Q
$$ \Rightarrow $$ $$4{N_0}{\left( {{1 \over 2}} ight)^{t/1}}$$ = $${N_0}{\left( {{1 \over 2}} ight)^{t/2}}$$
$$ \Rightarrow $$ $${2^{t/1}} = {4.2^{t/2}}$$
$$ \Rightarrow $$ t = 4 min
After 4 minutes, both P and Q have equal number of
nuclei.
$$ 	herefore $$ Number of nuclei of R
= $$\left( {4{N_0} - {{{N_0}} \over 4}} ight)$$ + $$\left( {{N_0} - {{{N_0}} \over 4}} ight)$$
= $${{9{N_0}} \over 2}$$

Answer

2 N
0

Answer

3 N
0

Answer

$${{9{N_0}} \over 2}$$

Answer

$${{5{N_0}} \over 2}$$

Atoms & Nuclei

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