Question

The half-life of radon-222 is 3.8 days. How many grams of radon-222 remain
after 15.2 days if the original amount was 6.00 g?
A. 0.750 g
B. 0.375 g
C. 1.20 g
D. 3.00 g

Answer 1

The mass of radon-222 that will remain after 15.2 days given that it was originally 6 g is 0.375 g (Option B)

What is half life?

This is the time taken for half a substance to decay.

How to determine the number of half-lives that has elapsed

We'll begin our calculation by calculating the number of half-lives that has elapsed after 15.2 days. This is illustrated below:

• Half-life (t½) = 3.8 days
• Time (t) = 15.2 day
• Number of half-lives (n) =?

n = t / t½

n = 15.2 / 3.8

n = 4

Thus, 4 half-lives has elapsed.

How to determine the amount remaining

• Original amount (N₀) = 6 g
• Number of half-lives (n) = 4
• Amount remaining (N) = ?

The amount of radon-222 remaining can be obtained as illustrated below:

N = N₀ / 2ⁿ

N = 6 / 2⁴

N = 6 / 16

N = 0.375 g

Thus, the amount of radon-222 remaining after 15.2 days is 0.375 g

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