!you have 200 g of a radioisotope. if the half-life of this radioisotope is 20 days, how many grams will remain after 40 days? show all your work or tell me how to do this! : )

We can use two equations for this problem.

t1/2 = ln 2 / λ = 0.693 / λ
Where t1/2 is the half-life of the element and λ is decay constant.

20 days = 0.693 / λ 
λ   = 0.693 / 20 days        (1) 

Nt = Nο eΛ(-λt)                (2)

Where Nt is atoms at t time, No is the initial amount of substance, λ is decay constant and t is the time taken.
t = 40 days

No = 200 g

From (1) and (2),
Nt =  200 g eΛ(-(0.693 / 20 days) 40 days)
Nt = 50.01 g

Hence, 50.01 grams of isotope will remain after 40 days.

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