Question

$\begin{array}{c}7/8\text{fraction of a sample disintegrates in t time.}\\ \text{How much time it will take to disintegrete}15/16\text{fraction :}\end{array}$

• A. $t$
• B. $\frac{4}{3}t$
• C. $\frac{5}{3}t$
• D. $2t$

Answer 1

The correct option is B $\frac{4}{3}t$

Solution we know

$ln\left(\frac{a_0}{a}\right)=kt$

where, $a_0\to$ initial sample

$a\to$ amount of sample left

after time t.

Here,

$ln\left(\frac{a_0}{a_0-\frac{7}{8}{a}_0}\right)=kt$

$\Rightarrow ln\left(8\right)kt$ ___(i)

So,

$ln\left(\frac{a_0}{a_0-\frac{75}{16}{a}_0}\right)=k{t}^{\prime }$

$\Rightarrow ln\left(16\right)=k{t}^{\prime }$____(ii)

Dividing (ii) by (i), we get

$\frac{t^{\prime }}{t}=\frac{ln\left(16\right)}{ln\left(8\right)}=\frac{4ln\left(2\right)}{3ln\left(2\right)}=\frac{4}{3}$

$t^{\prime }=4/3t$

option - B is correct.