After 3 days a sample of radon-222 has decayed to 58% of its original amount.

Question

After 3 days a sample of radon-222 has decayed to 58% of its original amount.
a) What is the half life of radon-222?
b) How long will it take the sample to decay to 20% of its original amount?

Answer 1

(a)

 

T = half life in days

 

t = days

 

A(t) = A₀ (0.5)^t/T

 

0.58 = (0.5)^3/T

 

log(0.58) = (3/T) log(0.5)

 

T = 3 log(0.5) / log(0.58) days ≅ 3.817 days

 

(b)

 

Solve for t in

 

0.20 = (0.5)^t/T = (0.5)^t/3.817

 

and get t in days.  Can you solve for t working with logarithms, and finish from here?