Answer to Question #275179 in Chemistry for janjan

Question

How much time will be required for a sample of H-3 to lose 75% of its radioactivity? The half-life of tritium is 12.26 years.?

Answer 1

Solution:

Tritium = H-3

The half-life (t_1/2) of tritium is 12.26 years.

From law of radioactive decay:

t_1/2 = ln(2) / λ

where λ = decay constant

λ = ln(2) / t_1/2

λ = (0.693) / (12.26 years) = 0.0565 years^-1

Radioactive decay follows the kinetics of a first order reaction:

ln[H-3]_t = -λt + ln[H-3]_o

If the sample lose 75% (0.75), then 25% (0.25) remains.

[H-3]_t = 0.25

[H-3]_o = 1.00

λ = 0.0565 years^-1

Therefore,

ln(0.25) = - (0.0565 years^-1) × t + ln(1.00)

-1.3863 = - (0.0565 years^-1) × t

t = (-1.3863) / (-0.0565) = 24.54 years

t = 24.54 years

Answer: 24.54 years will be required for a sample of H-3 to lose 75% of its radioactivity.