Question

22. Radon has a half-life of 3.83 days. How long will it take a 225 g sample to decay to 14.06 g? (3pts.)

Answer 1

Answer:

15.32 days

Explanation:

From the question given above, the following data were obtained:

Half-life (t½) = 3.83 days

Original amount (N₀) = 225 g

Amount remaining (N) = 14.06 g

Time (t) =.?

Next, we shall determine the number of half-lives that has elapsed. This can be obtained as follow:

Original amount (N₀) = 225 g

Amount remaining (N) = 14.06 g

Number of half-lives (n) =?

N = N₀ / 2ⁿ

14.06 = 225 / 2ⁿ

Cross multiply

14.06 × 2ⁿ = 225

Divide both side by 14.06

2ⁿ = 225 / 14.06

2ⁿ = 16

Express 16 in index form with 2 as the base

2ⁿ = 2⁴

n = 4

Thus, 4 half-lives has elapsed.

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

Half-life (t½) = 3.83 days

Number of half-lives (n) = 4

Time (t) =.?

n = t / t½

4 = t / 3.83

Cross multiply

t = 4 × 3.83

t = 15.32 days

Therefore the time for 225 g sample of Radon to decay to 14.06 g is 15.32 days