what is the total mass of rn-222 remaining in an original 160g sample after 19.1 days?
1 2.5g
2 5.0 g
3 10g
4 20g
how do you do this ?
To answer this question, we need to understand the concept of half-life and how it relates to the decay of radioactive substances.
The half-life of a radioactive substance is the time it takes for half of the initial sample to decay. In this case, the question is asking about the decay of Rn-222.
We can start by finding the number of half-lives that have occurred in the given 19.1 days. To do this, we divide the given time by the half-life of Rn-222, which is 3.82 days.
So, the number of half-lives (n) = 19.1 days / 3.82 days = 5 half-lives (rounded to the nearest whole number).
Each half-life reduces the amount of Rn-222 by half. Therefore, the remaining mass of the Rn-222 would be (1/2)^n times the initial mass of the sample.
Given that the initial mass of the sample is 160g, we can calculate the remaining mass of Rn-222 after 5 half-lives using the formula:
Remaining mass = (1/2)^n * Initial mass
Remaining mass = (1/2)^5 * 160g
Remaining mass = (1/32) * 160g
Remaining mass = 5g
So, the correct answer is option 1: 2.5g.