Question

How many half-lives must elapse until 84 % of a radioactive sample of atoms has decayed? -g?

Answer 1

Approximately 2.88 half-lives must elapse until 84% of the radioactive sample has decayed.

Step-by-step explanation:

The number of half-lives that must elapse until 84% of a radioactive sample of atoms has decayed can be determined by using the formula:

n = log(1 - f) / log(0.5)

where n represents the number of half-lives and f represents the fraction of atoms remaining. In this case, f is 0.16 (100% - 84% = 16%). Substituting this value into the formula, we get:

n = log(1 - 0.16) / log(0.5) ≈ 2.88

Therefore, approximately 2.88 half-lives must elapse until 84% of the radioactive sample has decayed.

Answer 2

Half-life is the time required for decay of 50% of radio-active nuclei.

Thus, when radio-active material crosses 1st half-life, 100/2 = 50% radio-active material is left and remaining 50% is elapsed.

When, when radio-active material crosses 2nd half-life, 50/2 = 25% radio-active material is left and remaining 75% is elapsed.

When radio-active material crosses 3rd half-life, 25/2 = 12.5% radio-active material is left and remaining 87.5% is elapsed.

Thus, 2 half-lives must elapse until 84 % of a radioactive sample of atoms has decayed.