Question

The half life of radon-222 is 3.8 days. How Much of a 100g sample is left after 15.2 days

Answer 1

After 15.2 days, which is equivalent to four half-lives of radon-222 (3.8 days each), a 100g sample of radon-222 would decay to 6.25 grams.

Step-by-step explanation:

The question pertains to the concept of radioactive decay and specifically the calculation of the remaining mass of a radioactive isotope (radon-222) after a certain period, given its half-life. Using the half-life of radon-222, which is 3.8 days, we can determine the amount of substance left after 15.2 days. Since 15.2 days is exactly four half-lives (15.2 / 3.8 = 4), we can calculate the remaining mass by halving the initial mass four times.

Mathematical calculation:
Initial mass = 100 g
After 1 half-life (3.8 days): 100g / 2 = 50 g
After 2 half-lives (7.6 days): 50g / 2 = 25 g
After 3 half-lives (11.4 days): 25g / 2 = 12.5 g
After 4 half-lives (15.2 days): 12.5g / 2 = 6.25 g

Therefore, after 15.2 days, 6.25 grams of the original 100 g sample of radon-222 would remain.

Answer 2

6.2 g

Explanation:

In a first-order decay, the formula for the amount remaining after n half-lives is

`N = (N_(0))/(2^(n))`

where

N₀ and N are the initial and final amounts of the substance

1. Calculate the number of half-lives.

If
`t_{(1)/(2)} = \text{3.8 da}`

`n = \frac{t}{t_{(1)/(2)}} = \frac{\text{15.2 da}}{\text{3.8 da}}= \text{4.0}`

2. Calculate the final mass of the substance.

`\text{N} = \frac{\text{100 g}}{2^(4.0)} = \frac{\text{100 g}}{16} = \text{6.2 g}`