find half-life of radioactive nuclide

Question

If 1.2 x 10⁵ atoms of a radioactive nuclide decay such that only 1.5 x 10⁴ atoms remained after 81days. the half-life of the radioactive nuclide is -------------------

Answer 1

It decays according to

 

A(t) = A₀(1/2)^t/T

 

A(t) = amount present at time t

A₀ = initial amount present (at t = 0)

t = elapsed time

T = half-life

 

t = 81 days

A(81) = 1.5 x 10⁴

A₀ = 1.2 x 10⁵

 

1.5 x 10⁴ = (1.2 x 10⁵)(1/2)^81/T

 

0.125 = (1/2)^81/T

 

ln(0.125) = (81/T)ln(1/2)

 

T = 81 ln(1/2) / ln(0.125) = 27 days

 

The half-life is 27 days.

 

Go ahead and test the solution.