Question

The half-life of radon-222 is 3.8 days. Calculate how long a 48g sample of radon will last before it contains only 3g of radon and stops being effective.

Answer 1

The duration it takes for a 48g sample of radon-222 to decay to 3g can be calculated using the half-life of radon-222, which is 3.8 days. The steps involve determining the number of half-lives required for the sample to reduce from 48g to 3g, solving for n, and then multiplying n by the half-life duration to get the total time.

Step-by-step explanation:

To calculate how long a 48g sample of radon-222 will last before it reduces to 3g, we use the concept of half-life, which, for radon-222, is 3.8 days. To determine the number of half-lives needed for the sample to decay from 48g to 3g, we use the following steps:

1. Determine the number of half-lives (n) using the formula:
   
2. Solve for n:
   
3. Calculate the total time by multiplying the number of half-lives by the half-life duration:
   

Using these steps will give us the total duration for when the radon sample becomes ineffective due to decay.