Question

the count rate of a radioactive source at t=0 was 1600 count/s and at t=8s it was 100 counts/s. The count rate (in counts) at t =6s was ----??

Answer 1

Hii friend,
Counting rate is nothing but the decay rate.

● Answer -
A6 = 200 counts/s

● Explanation -
# Given -
A0 = 1600 counts/s
A8 = 100 counts/s

# Solution -
Let T be half life of radioisotopes.

Decay rate is calculated by -
A = A0(1/2)^(t/T)

At t = 8,
100 = 1600 × (1/2)^(8/T)
2^(8/T) = 16 = 2^4

Comparing indexes -
8/T = 4
T = 2 s

At t = 6 s,
A6 = 1600 × (1/2)^(6/2)
A6 = 1600 / 8
A6 = 200 counts/s

Therefore, count rate at t = 6 s is 200 counts/s.




Hope this helped...