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 t…

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asked Apr 21, 2020 135k views

1 Answer

Forkdbloke · Answer 1 · 2020-04-25T23:19:08+0000

Answer:

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