Question

The masses of two radioactive substances are same and their half lives are $1$ year and $2$ years respectively. The ratio of their activities after six years will be

• A. $1:4$
• B. $1:2$
• C. $2:1$
• D. $4:1$

Answer 1

The correct option is A $1:4$

Number of half-life completed for first substance is $6/1=6$

Thus, Fraction left is $1/2^6=1/64$

Activity of first substance after six years is $=N_{left}\times \lambda \propto \frac{1}{64}\times \frac{ln2}{1}$

Number of half-life completed for second substance is $6/2=3$

Thus, Fraction left is $1/2^3=1/8$

The ratio of their activities after six years will be $1/2^6:1/2^3=8:64=1:8$

Activity of second substance after six years is $\propto \frac{1}{8}\times \frac{ln2}{2}$

Taking the ratio of activities, we get $1/64:1/16=1:4$