Question

How long will it take a sample of lead-212 (which has a half-life of 10.64 h) to decay to one-eighth its original strength?

Answer 1

Answer:

31.92 h

Explanation:

We'll begin by calculating the number of half-lives that has elapsed. This can be obtained as follow:

Original amount (N₀) = 1

Amount remaining (N) = ⅛

Number of half-lives (n) =?

N = 1/2ⁿ × N₀

⅛ = 1/2ⁿ × 1

Cross multiply

2ⁿ = 8

Express 8 in index form with 2 as the base.

2ⁿ = 2³

n = 3

Thus, 3 half-lives has elapsed.

Finally, we shall determine the time. This can be obtained as follow:

Half-life (t½) = 10.64 h

Number of half-lives (n) = 3

Time (t) =?

n = t / t½

3 = t / 10.64

Cross multiply

t = 3 × 10.64

t = 31.92 h

Therefore, it will take 31.92 h for lead-212 to decay to one-eighth its original strength.