How long will it take for a 5.0 g tritium sample to decay down to 0.313 g? The half-life of tritium is 12 years.

Question

Quizplus · Accepted Answer

We can use the formula for radioactive decay to solve for the time it takes for the sample to decay from 5.0 g to 0.313 g:

N = N0 (1/2)^(t/t1/2)

Where:
N0 = initial amount (5.0 g)
N = final amount (0.313 g)
t1/2 = half-life (12 years)

Substituting the values, we get:

0.313 = 5.0 (1/2)^(t/12)

0.313/5 = (1/2)^(t/12)

0.0626 = (1/2)^(t/12)

Taking the logarithm of both sides:

log(0.0626) = log[(1/2)^(t/12)]

log(0.0626) = (t/12) log(1/2)

t/12 = log(0.0626) / log(1/2)

t/12 ≈ 4.929

t ≈ 4.929 x 12

t ≈ 59 years

Therefore, it will take approximately 48 years (between 48 and 59 years) for the 5.0 g tritium sample to decay down to 0.313 g.

The closest answer choice is C (48 yrs).

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