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  • What is the half-life period of a radioactive material if its activity drops to <img alt="\mathrm{1 / 16^{\text {th }}}" src="https://entrancecorner.oncodecogs.com/gif.latex?%5Cmathrm%7B1%20/%2016%

What is the half-life period of a radioactive material if its activity drops to \mathrm{1 / 16^{\text {th }}} of its initial value in 30 years?

Option: 1

\mathrm{9.5 \text { years }}


Option: 2

\mathrm{8.5 \text { years }}


Option: 3

\mathrm{7.5 \text { years }}


Option: 4

\mathrm{10.5 \text { years }}


Answers (1)

best_answer

Activity of the material at time \mathrm{t} is,

\mathrm{A_t =A_0 2^{-t / T_{1 / 2}} }

\mathrm{\frac{A_0}{16} =A_0 2^{-30 / T_{1 / 2}} }

\mathrm{\frac{1}{2^4} =\frac{1}{2^{30} / T_{1 / 2}} }

\mathrm{T_{1 / 2} =7.5 \text { years }}

The half life period of a radioactive material is 7.5 year

Hence 3 is correct option.
 

Posted by

seema garhwal

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