The halflife of radium is 1690 years If 50 grams are present

The half-life of radium is 1690 years. If 50 grams are present now. how much will be present in 510 years? grams (Do not round until the final answer. Then round to the nearest thousandth as needed.)

Solution

general decay equation is N=N₀ e^-kt where N₀  is initial amount

halflife is 1690 years

N=(1/2)N₀

(1/2)N₀=N₀ e^-k*1690

e^-k*1690=1/2

-1690k=ln(1/2)

k=0.00041

N=N₀ e^-0.00041t

N₀=50 gm

amount after 510 years

N= 50e^-0.00041*510

N= 40.566 gm

amount after 510 years =40.566gm