An element has a half-life of 29 hours. If 100 mg of the element decays over a period of 58 hours, how many mg of the element will remain?
So far I have;
n= elapsed time/ half-life
=58/29
n=2
so
if 100 at t = 0
then 50 at t = 29
then 25 at t = 58
or 100* (1/2)^2 = 100 * 1/4 = 25
Thank you
You are welcome.
To find the amount of the element that will remain after 58 hours, you can use the formula for exponential decay:
N = N₀ * (1/2)^(n)
Where:
N: The remaining amount of the element
N₀: The initial amount of the element
n: The number of half-lives that have occurred
In this case, you have already calculated n as 2 because the elapsed time of 58 hours is twice the half-life of 29 hours.
Now, substitute the values into the equation:
N = 100 mg * (1/2)^(2)
Simplify:
N = 100 mg * (1/4)
N = 25 mg
Therefore, after 58 hours, 25 mg of the element will remain.