Question

If a rock started with 1,000 atoms of a parent but now contains 250 atoms, how many half lives have passed?

a. 0.5 half lives.
b. 1 half life.
c. 2 half lives.
d. 0.25 half lives.

Answer 1

Option C. 2 half lives.

Step-by-step explanation:

The following data were obtained from the question:

Original amount (N₀) = 1000 atoms

Amount remaining (N) = 250 atoms

Number of half-lives (n) =?

Half-life is defined as the time taken for the substance to reduce to half its original side. Mathematically, it can be obtained as follow:

N = 1/2ⁿ × N₀

N is the amount remaining.

n is the number of half-lives.

N₀ is the original amount.

Using the above formula, we can obtain the number of half-lives as follow:

Original amount (N₀) = 1000 atoms

Amount remaining (N) = 250 atoms

Number of half-lives (n) =?

N = 1/2ⁿ × N₀

250 = 1/2ⁿ × 1000

Cross multiply

250 × 2ⁿ = 1000

Divide both side by 250

2ⁿ = 1000/250

2ⁿ = 4

Express 4 in index form

2ⁿ = 2²

n = 2

Therefore, it will take two (2) half lives for the amount to get to 250 atoms.