Radon 86222Rn is a radioactive gas with a half-life of 3.82 d. If there are initially 400 decays/s in a sample, how many radon nuclei are left after 2 d ?
Please help, I don't understand how to do this.
To solve this problem, we need to understand the concept of half-life and how it relates to radioactive decay.
The half-life of a radioactive substance is the time it takes for half of the radioactive nuclei to decay. In this case, the half-life of radon-222 (86222Rn) is 3.82 days, which means that after 3.82 days, only half of the original number of radioactive nuclei will remain.
Here's how you can approach this problem:
Step 1: Calculate the number of half-lives that have passed
To calculate the number of half-lives that have passed, divide the given time by the half-life:
Number of half-lives = time / half-life
Number of half-lives = 2 days / 3.82 days ≈ 0.523 half-lives
Step 2: Calculate the remaining fraction of radioactive nuclei
Since half of the radioactive nuclei decay after one half-life, the remaining fraction after 0.523 half-lives can be calculated as:
Remaining fraction = (1/2)^(number of half-lives)
Remaining fraction ≈ (1/2)^(0.523) ≈ 0.746
Step 3: Calculate the number of remaining radioactive nuclei
To find the number of remaining radioactive nuclei, multiply the remaining fraction by the initial number of radioactive nuclei:
Remaining number of nuclei = remaining fraction * initial number of nuclei
Remaining number of nuclei ≈ 0.746 * 400 decays/s
Remaining number of nuclei ≈ 298.4 decays/s
So, after 2 days, there are approximately 298.4 radon nuclei left in the sample.
It's important to note that this calculation assumes exponential decay and that the decay rate remains constant over time.
The half-life is 3.82 days
That means that every time 3.82 days have passed, 1/2 of it is gone. So, starting with 400 nuclei, after 2 days there will be
400(1/2)^(2/3.82) = 278