2. After 10 years, a 100 mg sample of argon-42 has decayed to 81 mg. Estimate the half-life of argon-42.

Answer 1

To estimate the half-life of argon-42, we can use the formula for exponential decay:

N(t) = N0 * (1/2)^(t/T)

where:
- N(t) is the amount of substance remaining after time t
- N0 is the initial amount of substance
- T is the half-life
- t is the time elapsed

From the given information:
- N(10) = 81 mg
- N0 = 100 mg
- t = 10 years

Plugging these values into the formula, we get:

81 = 100 * (1/2)^(10/T)

0.81 = (1/2)^(10/T)

Taking the logarithm of both sides to solve for T:

-0.093421 = (10/T) * log(1/2)

-0.093421 = (10/T) * -0.3010

T = 0.3099 years

Therefore, the estimated half-life of argon-42 is approximately 0.31 years.