Question

If you are given:

The duration of the half-life in years
The amount of original isotope
The amount of remaining isotope
Explain how you would find the age of the sample:
"

Answer 1

n = A / A0 where n is the fraction of the sample remaining

If T is the half-life then

A = T^n * A0 = (1/2)^n A0

This is easy if A / A0 = 1/2, 1/4, 1/8, or 1/16 = 1/2*n where n is integral

Otherwise,

ln (A / A0) = -n ln 2 = -.693 n

Suppose 1000 = amt remaining and 10000 was initially present

Then ln A / A0 = .1 (more than 3 but less than 4 half-lives)

n = -ln .1 / .693 = 3.32

n^3.32 = .1 where n is the number of half=lives