A sample of has an original mass of 57.3 mg,and after 24.0 hours the sample mass is 15.6 mg.1.88 half-lives correspond to 27.2% of the sample remaining.What is the half-life of ?

Question

A sample of  has an original mass of 57.3 mg,and after 24.0 hours the sample mass is 15.6 mg.1.88 half-lives correspond to 27.2% of the sample remaining.What is the half-life of  ?

Quizplus · Accepted Answer

We can use the formula for radioactive decay:
N(t) = N₀(1/2)^(t/T)
where N(t) is the amount of sample remaining after time t, N₀ is the initial amount, T is the half-life, and t is the elapsed time.

From the problem, we know that:
- N₀ = 57.3 mg
- N(24.0 hr) = 15.6 mg
- 1.88 half-lives correspond to 27.2% remaining

Using the formula and solving for T, we get:
N(24.0 hr) = N₀(1/2)^(24.0/T)
15.6 = 57.3(1/2)^(24.0/T)
(1/2)^(24.0/T) = 15.6/57.3
(1/2)^(2.4/T) = 0.272
2.4/T = log(0.272)/log(1/2)
T = 12.8 hr

Therefore, the half-life of the sample is 12.8 hours, which corresponds to choice (C).

A Sample of Has an Original Mass of 57