Question

The radioactive nuclides A and B have half life of $t$ and $2t$ respectively. If we start an experiment with one mole of each of them, the mole ratio after time interval of $6t$ will be

• A. $1:2$
• B. $1:8$
• C. $1:6$
• D. $1:1$

Answer 1

Answer: (B)

$1:8$

Using formula: $\lambda =\frac{ln2}{t_{\frac{1}{2}}}$

${\lambda }_A=\frac{ln2}{t}and{\lambda }_B=\frac{ln2}{2t}$

From integrated rate law:

$N=N_0{e}^{-\lambda t}$

$N_0=$ 1 mole for each of them

Moles left of A after $6t=e^{-\lambda 6t}=e^{\frac{-ln2}{t}\times 6}=\frac{1}{2^6}$

Moles left of B after $6t=e^{\frac{-ln2}{2t}\times 6t}=e^{-ln{2}^3}=\frac{1}{2^3}$

Ratio of moles left of A:B $=\frac{1}{2^6}:\frac{1}{2^3}=1:2^3=1:8$