You have a radioactive sample with a half-life of 1 hour. At t = 1 hour, a Geiger counter measures its radiation at 40 counts/minute. At t = 4 hours, it measures 5 counts/minute. Fill in the table for the activity at the unknown times (in counts/minute).
Time Geiger Counter Radiation Rate
0 hours
1 hour 40 counts/minute
2 hours
3 hours
4 hours 5 counts/minute

Explanation:

Given that, .

The half-life of a radioactive element is

t½ = 1 hr.

At the first hour, the radioactive element has 40 counts/minute

After 4 hours it has 5 counts/minute

So,

We want to filled the table.

0 hours, I.e at the start

40 counts/mins × 2 = 80 counts / mis

First half-life (first hour) is

40 counts/mins

Second half-life (second hour)

40 counts/mins × ½ = 20 counts/mins

Third half-life (third hour)

40 counts/mins × ¼ = 10 counts / mins

Fourth half life (fourth hour)

40 counts/mins × ⅛ = 5 counts / mins

So, the table is

TimeGeiger Counter Rate

0 hours 80 counts / minutes

1 hour 40 counts / minutes

2 hours 20 counts / minutes

3 hours 10counts / minutes

4 hours 5 counts / minute