Question

Which of the following relation is correct? ($t_{1/2}$ and $t_{3/4}$ are time required to complete half and 3/4 decay respectively)

• A. $t_{1/2}=2\times t_{3/4}$
• B. $t_{1/2}=3\times t_{3/4}$
• C. $t_{3/4}=2\times t_{1/2}$
• D. $t_{3/4}=3\times t_{1/2}$

Answer 1

The correct option is C $t_{3/4}=2\times t_{1/2}$

As we know, the integrated rate law expression is

$t=\frac{2.303}{\lambda }\log \frac{N_0}{N}$

For $t=t_{1/2}$,

$N=\frac{N_0}{2}$
Hence, the half life period is $t_{1/2}=\frac{2.303}{\lambda }\log \frac{N_0}{N_0/2}$ ..... (1)

When

$t=t_{3/4}$, three fourth of the decay process is complete and $N=\frac{N_0}{4}$

$t_{3/4}=\frac{2.303}{\lambda }\log \frac{N_0}{N_0/4}$ ...... (2)

Divide equation (2) by equation (1)

$\frac{t_{3/4}}{t_{1/2}}=\frac{log\frac{N_0}{N_0/4}}{log\frac{N_0}{N_0/2}}=2$

$\therefore t_{3/4}=t_{1/2}\times 2$