Answer:
m = 25 g
Explanation:
To do this, we need to use the general expression for Half life:
A = Ao e^-tλ (1)
Where:
A: concentration or mass of the substance after t time has passed
Ao: Initial concentration or mass of the substance
t: time that has passed.
λ: lambda that is relationed to half life time.
The value of λ can be calculated with the following expression:
λ = ln2 / t(1/2) (2)
So, let's calculate first the value of lambda, and then, we replace it in expression (1) to know the mass of the radioisotope:
λ = ln2/100
λ = 6.93x10^-3
Now, let's use (1) to calculate the mass after 200 years:
m = 100e^(-200*6.93x10^-3)
m = 100e^(-1.386)
m = 25 g
And this is the mass of the isotope after 200 years.
