Answer:
You calculate the half-life from the amount of material that disappears in a given time.
Explanation:
Half-life (t½) is the time required for the nuclei to decay to half of the original amount.
Radioactive nuclei decay according to the equation:
Equation 1: Nt/N0=e^-λt, where
N0 is the initial number of nuclei at time t=0
Nt is the number of nuclei that remain after time t. We can also use any number that is proportional to the number of nuclei, such as mass or disintegration counts.
λ is a constant called the decay constant. Each nucleus has its own decay constant.
The equation for half-life is
Equation 2: t1/2=in2/λ
We can combine these two equations to get
Equation 3: Nt/N0=0.5^t/t½
EXAMPLE:
A 50 g sample of radium–226 decays to 5.7 g after 5000 years. What is the half-life of radium–226?
Solution:
Let’s use Equation 3:
Nt/N0=0.5^t/t½
5.7g/50g=0,5^5000yr/t1/2
0.114=0.5^5000yr/t1/2
Take the natural logarithm of each side
In 0.114= 5000yr/t1/2 × In 0.5
-2.7= 5000yr/t1/2 × (-0.693)
t1/2= (5000yr × 0.693/2.17) = 1600yr
The half-life of radium–226 is 1600 yr.
