- Home
- Standard 12
- Physics
13.Nuclei
medium
If $20\, gm$ of a radioactive substance due to radioactive decay reduces to $10 \,gm$ in $4 \,minutes,$ then in what time $80\, gm $ of the same substance will reduce to $10 \,gm$
A
In $8 \,minutes$
B
In $12\, minutes$
C
In $16\, minutes$
D
In $20\, minutes$
Solution
(b) $20\, gm$ substance reduces to $10\, gm$ ($i.e.$ becomes half in $4\, min.)$
So ${T_{1/2}} = 4\,\min $.
Again $M = {M_0}{\left( {\frac{1}{2}} \right)^{t/{T_{1/2}}}}$
==> $10 = 80\,{\left( {\frac{1}{2}} \right)^{t/4}}$
==>$\frac{1}{8} = {\left( {\frac{1}{2}} \right)^3} = {\left( {\frac{1}{2}} \right)^{t/4}}$
==>$ t = 12\, min.$
Standard 12
Physics