Question

7/8 fraction of a sample disintegrates in 't' time, how much time it will take to disintegrate 15/16 fraction ?

• A. t
• B. 4/3 t
• C. 5/3 t
• D. 2t

Answer 1

The correct option is B 4/3 t

After the disintegration of $7/8$, the fraction of the remaining amount is $\frac{N}{N_0}=1-\frac{7}{8}=1/8$..................(1)

where $N_0$ is the initial amount.

Using following relation $N=N_0(\frac{1}{2}{)}^n$........(2)with equation-1 we get $n=3$

But $n=\frac{t}{t_{1/2}}$ so half life $t_{1/2}=t/3$

After disintegration 15/16 the fraction remaining amount $\frac{N}{N_0}=1-\frac{15}{16}=1/16$

So using it in the eqaution-2, we get $n=4$

So time needed will be $n\times t_{1/2}=4t/3$

Option B is correct.