Question

The half-life of a radioactive substance is $6$ hours. The amount of the substance that has disintegrated when $36$ gm of it undergoes decay for 18 hours is

• A. $31.5gm$
• B. $4.5gm$
• C. $18gm$
• D. $9gm$

Answer 1

The correct option is A $31.5gm$

Half life $=$6 hours
After 3 half lives, i.e., 18 hours, fraction of substance left $=(\frac{1}{2}{)}^3=\frac{1}{8}$
Fraction undergone decay $=1-\frac{1}{8}=\frac{7}{8}$
Amount of decayed substance $=\frac{7}{8}\times 36gms=31.5gms$