Question

If the half lives of a radioactive element for $\alpha$ and $\beta$ decay are $4$ years and $12$ years respectively, then the percentage of the element that remains after $12$ years will be

• A. $6.25$ %
• B. $12.5$ %
• C. $25$ %
• D. $50$ %

Answer 1

Answer: (A)

$6.25$ %

Number of half-life completed due to $\alpha$ decay is $12/4=3$

Number of half-life completed due to $\beta$ decay is $12/12=1$

So total number of half-life completed is $3+1=4$

So the percentage of the element that remains after $12$ years will be

$100/2^4=100/16=6.25\%$