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Standard XII

Chemistry

Relation Between r and a

The radioacti...

Question

The radioactive nucleus A and B have half lives 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.

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Solution

$N = {(\frac{1}{2})}^{\frac{t}{t_{1 / 2}}}$

For A-

$N_{A} = {(\frac{1}{2})}^{\frac{6 t}{t}} = \frac{1}{64}$

For B-

$N_{B} = {(\frac{1}{2})}^{\frac{6 t}{2 t}} = \frac{1}{8}$

Hence,

$\frac{N_{A}}{N_{B}} = \frac{1}{8}$

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The radioactive nucleus A and B have half lives 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.

N=(12)tt1/2For A-NA=(12)6tt=164For B-NB=(12)6t2t=18Hence,NANB=18

$N = {(\frac{1}{2})}^{\frac{t}{t_{1 / 2}}}$

For A-

$N_{A} = {(\frac{1}{2})}^{\frac{6 t}{t}} = \frac{1}{64}$

For B-

$N_{B} = {(\frac{1}{2})}^{\frac{6 t}{2 t}} = \frac{1}{8}$

Hence,

$\frac{N_{A}}{N_{B}} = \frac{1}{8}$