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

The half-life of the material is 2 years

Step-by-step 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 = (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 = (N_o)/((t/2)^2) \\\\500 = (2000)/((t/2)^2)\\\\(t/_2)^2 = (2000)/(500) \\\\(t/_2)^2 = 4\\\\t/_2 = √(4) \\\\t/_2 = 2 \ years`

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