Question

How long will it take for the 1.35-mg sample of 236Pu in Example 19.4 to decay to 0.100 mg? (The half-life of plutonium-236 is 2.86 yr.) Express the time in years to three significant figu

Answer 1

10.7 years

Explanation:

The decay equation can be written as ...

remaining = initial × (1/2)^(t/(half-life))

Filling in the given values, we can solve for t.

0.100 = 1.35 × (1/2)^(t/2.86)

0.100/1.35 = (1/2)^(t/2.86) divide by 1.35

Taking logs transforms this to a linear equation:

log(0.100/1.35) = (t/2.86)log(1/2)

Since log(a/b) = -log(b/a), we can multiply both sides by -1 and simplify the logs a bit.

log(1.35/.1) = t·(log(2)/2.86)

2.86·log(13.5)/log(2) = t ≈ 10.7 . . . . years

The decay time is about 10.7 years.