Problema Solution
the half life of a certain substance is 30 years. How long will it take for a sample of this substance to decay to 78% of its original amount.
Answer provided by our tutors
The model for radioactive decay is:
A(t) = A0 (1/2)^(t/h)
A0 = is the initial sample
h = 50 years the half-life
t = time in years
In our case the formula is:
A = A0(1/2)^(t/30)
We need to find t such that A(t) = 0.78A0 that is:
0.78*A0 = A0 (1/2)^(t/30)
A0 (1/2)^(t/30) = 0.78A0
(1/2)^(t/30) = 0.78
(t/30) log(1/2) = log(0.78)
........
........
t = 10.75 years
It will take 10.75 years for a sample of this substance to decay to 78% of its original amount.