Question

Initially 100 milligrams of a radioactive substance was present. After 6 hours the mass had decreased by 4%. If the rate of decay is proportional to the amount of the substance present at time t, find the amount remaining after 24 hours. (Round your answer to one decimal place.)

Answer 1

84.96 mg

Explanation:

No = 100 mg

t = 6 hours, N = 96% of No = 96 / 100 No

t = 24 hours, N = ?

Let after 24 hours the remaining part is N.

Use the decay law equation

N = No e^-λt

96 / 100 = e^-6λ

0.96 = e^-6λ

taking natural log on both the sides

ln 0.96 = - 6λ

λ = 6.8 x 10^-3 per hour

Now,

N = No e^-24λ

N = No x e^-(24 x 6.8 x 10^-3)

N = No (0.8496)

N = 100 x 0.8496 = 84.96 mg