Question

An unknown radioactive sample is observed to decrease in activity by a factor of two in a three hour period. What is its half-life?

Answer 1

Activity of radioactive sample after time 't' is given by:

R = R0*e^(-*t)

= decay constant = (ln 2)/T_half

R0 = Initial activity

R = Activity after 3 hr = R0/2

t = 3 hr

So,

R0/2 = R0*e^(-3*ln (2)/T_half)

e^(-3*ln (2)/T_half) = 1/2

-3*ln (2)/T_half = ln (1/2)

-3*ln (2)/T_half = -ln (2)

3/T_half = 1

T_half = 3 hr = Half-life of sample.

Remember that half-life is the time taken by radioactive sample to decrease it's activity by a factor of two.

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