Question

mohneys helpful info for #12. background radiation is the radiation that would exist in the laboratory even if the radioactive sample was not present.

1. a student measures the count rate of a radioactive sample with time in a laboratory. the background count in the laboratory is 30 counts per second.

count rate / counts per second	time / s
90	20

what is the time at which the student measures a count rate of 45 counts per second?
a. 30s
b. 40s
c. 60s
d. 80s

Explanation:

Step1: Subtract background count

Sample count at t=0: $150 - 30 = 120$ counts/s
Sample count at t=20s: $90 - 30 = 60$ counts/s

Step2: Determine half-life value

The sample count halves from 120 to 60 in 20s, so half-life $t_{1/2}=20$s.

Step3: Find target sample count

Target total count = 45 counts/s, so sample count: $45 - 30 = 15$ counts/s

Step4: Calculate time to reach target

Start at 120 counts/s:
After 1 half-life (20s): 60 counts/s
After 2 half-lives (40s): 30 counts/s
After 3 half-lives (60s): 15 counts/s

Answer:

C. 60s