Radioactive decay

Question

The half life for the radioactive decay of 32P is 14.3 days. How many days would be required for a couple of radio pharmaceutical containing 32P to decrease to 20% of it's initial activity? 

Answer 1

Another way to solve this is to work it as an exponential decay problem.

 

T_1/2 = 14.3 days

 

0.5 = 1e^-14.3k

 

k = -ln(0.5) / 14.3 ≅ 0.048472 days^-1

 

You want to solve for when 0.20 of the starting amount remains.

 

0.2 = 1 e^-kt = e^-0.048472t

 

t = -ln(0.2) / 0.048472 days ≅ 33.203 days

Answer 2

A = a₀(0.5)^t/h

 

0.2a₀ = a₀(0.5)^t/14.3

0.2 = (0.5)^t/14.3

ln 0.2 = (t/14.3) ln (0.5)

-1.6094 ≈ (t/14.3) (-0.6931)

-23.0144 ≈ -0.6931 t

33.2050 ≈ t