During the nuclear explosion, one of the product of ${ }^{90} \mathrm{Sr}$ with half life of 6.93 years. If 1 $\mu \mathrm{g}$ of ${ }^{90} \mathrm{Sr}$ absorbed in the bones of newly born baby in place of Ca, how much time, in years is required to reduce it by $90 \%$ if it is not lost metabolically

JEE Main · 2020 · 07 Jan 2020 · Shift 1 · Chemical Kinetics

During the nuclear explosion, one of the product of

^{90} Sr

with half life of 6.93 years. If 1

μ g

^{90} Sr

absorbed in the bones of newly born baby in place of Ca, how much time, in years is required to reduce it by

90%

if it is not lost metabolically

Answer: 23.03

Radioactive decay is first order, so reducing the amount by

90%

leaves

10%

and takes

t = \frac{l n ( 100/10 )}{l n 2} t_{1/2} = \frac{l n 10}{l n 2} t_{1/2}

. With

t_{1/2} = 6.93

years,

t = \frac{2.303}{0.693} \times 6.93 \approx 23.03

years.

JEE Main · 2020 · 07 Jan 2020 · Shift 1 · Numerical answer