Question

ln [A] - ln [A]0 = - k t 0.693 = k t1/2 Show the calculation of the decay constant (k) and the half-life (t1/2) of a radioactive nucleus if 44.3% of the material has decayed in 365 days.

Answer 1

When the amount of compound is given in %, we take as initial concentration 100%. The [A] is the amount of compound that remains. So in this case 44,3% of the material has decayed, this means that we still have 100-44.3 of the material, 55.7%.

Ln 55.7 - Ln100= -k x 365days

k= 1.6x10^-3 days^-1

Now fo the half-life:

0.693= 1.6x10^-3 days^-1 x t1/2

t1/2= 432.2 days

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