A certain sample of a radioactive material decays at a rate

A certain sample of a radioactive material decays at a rate of 213 per second at t= 0 At t = 20 minutes, the counting rate has fallen to 123 per second, What is the half-life of the sample? What is its decay constant? What will be the decay rate at t = 105 minutes?

Solution

A. ao = 213 per second at t = 0

a = 123 per sec, at t = 20 min

a = ao*exp(-lambda*t)

123 = 213*exp(-0.693*20/t_1/2)

ln(123/213) = -0.693*20/t_1/2

t_1/2 = -0.693*20/[ln(123/213)] = 25.24 min

B. lambda =0.693/t_1/2 = 0.693/25.24 = 2.74*10^-2 per min

C. a = ao*exp(-lambda*t) = 213*exp(-274*10^-2 min^-1 * 105 min) = 11.99 per sec

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