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  • A and B are two radioactive substances whose half lives are 1 and 2 years respectively. Initially 10 gm of A and 1 gm of B is taken. The time (approximate) after which they will have same quantity

A and B are two radioactive substances whose half lives are 1 and 2 years respectively. Initially 10 gm of A and 1 gm of B is taken. The time (approximate) after which they will have same quantity remaining is –

Option: 1

6.62 years


Option: 2

5 years


Option: 3

3.2 years 


Option: 4

7 years


Answers (1)

best_answer

\begin{array}{cc|c} & \mathrm{A} & \mathrm{B} \\ \mathrm{T}_{1 / 2} & 1 \text { year } & 2 \text { year } \\ \mathrm{M}_0 & 10 \mathrm{gm} & 1 \mathrm{gm} \\ \mathrm{t}=? & \mathrm{M} & \mathrm{M} \end{array}

M=\frac{10}{2^{t / 1}}             ..........(i)

M=\frac{1}{2^{t / 2}}            ..........(ii)

\frac{10}{2^t}=\frac{1}{2^{t / 2}}

\text { or } 2^{t / 2}=10 \text { (taking log both side) }

\log 2^{t / 2}=\log 10

\frac{t}{2} \log _{10} 2=\log _{10} 10

\therefore \mathrm{t}=2 / 0.3010=6.62 \text { year }

Posted by

Sanket Gandhi

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