Question

Suppose you have 100 grams of a radioisotope with a half-life of 100 years. How much of the isotope will you have after 200 years?

Answer 1

Amount Remaining Years #half lives
100g 0 0
50 g 100 1
25g 200 2

Answer 2

m = 25 g

Step-by-step 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.