Question

The decay of a radioactive material is monitored using a Geiger counter. At the start, the count rate is 2000 decays/minute. Four hours later the decay rate is 500 counts/min. What is the half-life of the material?

Answer 1

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;

$N = \frac{N_o}{(t/2)^2} \\\\N_o-is \ the \ initial \ count\ rate\\\\N-is \ the \ final \ count\ rate\\\\t/_2 - is \ the\ half\ life \\\\N = \frac{N_o}{(t/2)^2} \\\\500 = \frac{2000}{(t/2)^2}\\\\(t/_2)^2 = \frac{2000}{500} \\\\(t/_2)^2 = 4\\\\t/_2 = \sqrt{4} \\\\t/_2 = 2 \ years$

Therefore, the half-life of the material is 2 years