JEE MAIN - Chemistry (2007 - No. 24)
A radioactive element gets spilled over the floor of a room. Its half-life period is 30 days. If the initial
activity is ten times the permissible value, after how many days will it be safe to enter the room?
1000 days
300 days
10 days
100 days
Explanation
Suppose activity of safe working $$=A$$
Given $${A_0} = 10A$$
$$\lambda = {{0.693} \over {{t_{1/2}}}} = {{0.693} \over {30}}$$
$${t_{{\raise0.5ex\hbox{$\scriptstyle 1$} \kern-0.1em/\kern-0.15em \lower0.25ex\hbox{$\scriptstyle 2$}}}} = {{2.303} \over \lambda }\log {{{A_0}} \over A}$$
$$ = {{2.303} \over {0.693/30}}\log {{10A} \over A}$$
$$ = {{2.303 \times 30} \over {0.693}} \times \log 10$$
$$ = 100$$ days.
Given $${A_0} = 10A$$
$$\lambda = {{0.693} \over {{t_{1/2}}}} = {{0.693} \over {30}}$$
$${t_{{\raise0.5ex\hbox{$\scriptstyle 1$} \kern-0.1em/\kern-0.15em \lower0.25ex\hbox{$\scriptstyle 2$}}}} = {{2.303} \over \lambda }\log {{{A_0}} \over A}$$
$$ = {{2.303} \over {0.693/30}}\log {{10A} \over A}$$
$$ = {{2.303 \times 30} \over {0.693}} \times \log 10$$
$$ = 100$$ days.