The half life of radon 222 is 3.82 days. If the initial mass of a sample of radon 222 is 198.72 grams, how much will remain after 19.25 days?
Yes
To determine how much radon 222 will remain after 19.25 days, we can use the formula for exponential decay:
N(t) = N₀ * (1/2)^(t/h)
Where:
N(t) is the amount remaining after time t,
N₀ is the initial amount,
t is the elapsed time, and
h is the half-life.
Let's substitute the given values into the formula:
N(t) = 198.72 * (1/2)^(19.25/3.82)
Now we can calculate the result.
To calculate how much radon-222 will remain after a certain number of days, we need to use the concept of exponential decay. The half-life of radon-222 is given as 3.82 days, which means that every 3.82 days, the amount of radon-222 will be halved.
We can use the formula for exponential decay to calculate the amount remaining:
N(t) = N₀ * (1/2)^(t / T)
where:
- N(t) is the amount remaining after time t
- N₀ is the initial amount
- t is the time that has passed
- T is the half-life of the substance
In this case, N₀ (the initial mass) is given as 198.72 grams, and the time that has passed is 19.25 days. We need to find N(19.25), the amount remaining after 19.25 days.
Let's substitute the given values into the formula:
N(19.25) = 198.72 * (1/2)^(19.25 / 3.82)
To solve this mathematically, we can calculate (1/2)^(19.25 / 3.82) first, and then multiply it by 198.72.
Calculating (1/2)^(19.25 / 3.82):
(1/2)^(19.25 / 3.82) ≈ 0.012
Now, multiply this value by 198.72:
N(19.25) ≈ 0.012 * 198.72 ≈ 2.38 grams
Therefore, approximately 2.38 grams of radon-222 will remain after 19.25 days.
after t days, the amount remaining will be
198.72 * (1/2)^(t/3.82)
Now just plug in the number of days you need.