Question

Complete the following table for a radioactive element whose half life is $5$ minutes. Assume that you have $32$g of this element at start, i.e., at t$=0$.

Time 't' in minutes	$0$	$5$	$10$	$15$	$20$	$25$
Amount of radioactive element left in grams	$32$

Answer 1

Given : $T_{1/2}=5$ minutes
Amount of radioactive substance initially $N_o=32g$
Amount of substance remaining after time $t$, $N=\frac{N_o}{2^n}=\frac{32}{2^n}$
where $n=\frac{t}{T_{1/2}}=\frac{t}{5}$
At $t=5$ :
We get $n=\frac{5}{5}=1$ $⟹N=\frac{32}{2}=16g$
At $t=10$ :
We get $n=\frac{10}{5}=2$ $⟹N=\frac{32}{2^2}=8g$
At $t=15$ :
We get $n=\frac{15}{5}=3$ $⟹N=\frac{32}{2^3}=4g$
At $t=20$ :
We get $n=\frac{20}{5}=4$ $⟹N=\frac{32}{2^4}=2g$
At $t=25$ :
We get $n=\frac{25}{5}=5$ $⟹N=\frac{32}{2^5}=1g$