Question

If $10$ % of a radioactive substance decays in every $5$ years, then the percentage of substance that will decayed in $20$ years will be

• A. $40$ %
• B. $50$ %
• C. $65.6$ %
• D. $34.4$ %

Answer 1

The correct option is D $34.4$ %

The undecayed substance after $5$ years is $100-10=90\%$

After $20$ years, i.e., $4\times 5$ years, undecayed fraction is $90\%of90\%of90\%of90\%=0.9\times 0.9\times 0.9\times 0.9=0.656$

So fraction decayed is $1-0.656=0.344,i.e,34.4\%$