The half- life for beta decay of strontium- 90 is 28.8 years. A milk sample is found to contain 10.3 ppm strontium- 90. How many years would pass before the strontium- 90 concentration would drop to 1.0 ppm?

Question

Quizplus · Accepted Answer

We can use the formula for radioactive decay:
N = N0 * (1/2)^(t/T)
where N is the final concentration (1.0 ppm), N0 is the initial concentration (10.3 ppm), t is the time elapsed, and T is the half-life (28.8 years).

Plugging in the values, we get:
1.0 = 10.3 * (1/2)^(t/28.8)
Taking the natural logarithm of both sides:
ln(1.0/10.3) = (t/28.8) * ln(1/2)
Solving for t:
t = ln(1.0/10.3) * 28.8 / ln(1/2)
t ≈ 96.9 years

Therefore, the answer is C.

The Half- Life for Beta Decay of Strontium- 90 Is