Question

If+a+substance+has+a+half+life+of+520+years,+and+you+start+off+with+1,000+g+of+it.+it+is+the+year+2021,+how+much+will+i+have+left+in+the+year+3061

Answer 1

`A=250g`

Step-by-step explanation:

Hello there!

In this case, by considering the radioactive decay as a first-order kinetic model:

`A=Ao*exp(-kt)`

We can firstly calculate the rate constant given the half life:

`k=(ln(2))/(t_(1/2)) =(ln(2))/(520years)=1.33x10^(-3)years^(-1)`

Thus, we can plug in the elapsed time and the initial amount Ao to obtain:

`A=1,000g*exp[-1.33x10^(-3)years^(-1) *(3061-2021)years]\\\\A=250g`

Best regards!