A radioactive element decays with a half-life of 9 years. if a mass of the element weighs 6 pounds at t=0, find the amount of the element after 11.5 years.

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06-09-2022
Physics

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A radioactive element decays with a half-life of 9 years. if a mass of the element weighs 6 pounds at t=0, find the amount of the element after 11.5 years.

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Aditmarkas98idn Aditmarkas98idn · Answer 1 · 2022-09-12T01:58:21-04:00

By the half-life of radioactive, the remaining mass of radioactive elements is 2.47 pounds.

We need to know about the half-life of the radioactive elements to solve this problem. The radioactive element will decay over time and follow the equation

N = No(1/2)^(t/t'')

where N is the final quantity, No is the initial quantity, λ is the decaying constant, t is time and t'' is the half-life of a radioactive element.

From the question above, we know that

t'' = 9 years

No = 6 pounds

t = 11.5 years

Calculate the remaining mass

N = No(1/2)^(t/t'')

N = 6(1/2)^(11.5/9)

N = 2.47 pounds

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