Question

The half-life of plutonium 239 is 24,200 years. Assume that the decay rate is proportional to the amount. Determine the amount of time it would take 3 grams of radium to decay to 2 grams. Round to the nearest hundred.

Answer 1

time taken is equal to 14,156 years

Step-by-step explanation:

we know,

`Y=Ae^(-kt)`

at t = 0

Y(0) = A

given that half life of plutonium 239 = 24,200

`(A)/(2)=Ae^(-kt)\\0.5=e^(-kt)\\k* 24200 = ln(2)\\k = ( ln(2))/(24200)`

`Y=Ae^(-kt)`

`(3)/(2) = e^(-kt)\\ln(1.5)=-( ln(2))/(24200)* t\\t=-(ln(1.5)* 24200)/( ln(2))\\t=14,156 \ years`

hence time taken is equal to 14,156 years