the half life of radium-226 is 1590. after how many years will only 50 mg remain

Question

campbell_st · Answer

do you have a growth or decay model for radium...?

anonymous · Answer

the first part of the question is "if a sample has a mass of 150 mg find the mass that will remain after 1000 years" i did that part and got 96.9 mg remain

campbell_st · Answer

ok... so you have the model... I don't know what it is... but I'll use exponential just for the purpose of demonstrating


so you have 50mg remaining and k is the decay constant

$$50 = 150 e^{-kt}$$

then divide both sides by 150

$$\frac{1}{3} = e^{-kt}$$


now take the base e log of both sides

$$\log_{e}(\frac{1}{3}) = -kt$$

divide both sides of the equation by -k


so the time take for 150mg or radium to decay to 50mg is 

$$t = \frac{\log_{e}(\frac{1}{3})}{-k}$$

hope it makes sense....

anonymous · Answer

thanks it helped a lot i got it