Answer:
The half-life of the material is 2 years
Explanation:
Given;
initial count rate = 2000 decays/minute
final count rate = 500 counts/min
decay time = Four hours
To determine the half life of the material; we create a simple decay table that matches the decay time and count rates.
time (years) count rate
0 2000 decays/minute
2 1000 decays/minute
4 500 decays/minute
Half life is the time intervals = 2 years
Also using a formula;
[tex]N = \frac{N_o}{(t/2)^2} \\\\N_o-is \ the \ initial \ count\ rate\\\\N-is \ the \ final \ count\ rate\\\\t/_2 - is \ the\ half\ life \\\\N = \frac{N_o}{(t/2)^2} \\\\500 = \frac{2000}{(t/2)^2}\\\\(t/_2)^2 = \frac{2000}{500} \\\\(t/_2)^2 = 4\\\\t/_2 = \sqrt{4} \\\\t/_2 = 2 \ years[/tex]
Therefore, the half-life of the material is 2 years
