A radioactive material initially is observed to have an activity of 1000 decays/sec.If nine hours later it is observed to have an activity of 125 decays/s,what is its half-life?
A) 1/2 hour
B) 8 hours
C) 3 hours
D) 1 hour

Question

Quizplus · Accepted Answer

The formula for radioactive decay is:

N(t) = N0 * (1/2)^(t/T)

Where:
N(t) is the activity at time t
N0 is the initial activity
T is the half-life
t is the elapsed time

Using the given values:

N0 = 1000 decays/sec
N(t) = 125 decays/sec
t = 9 hours

125 = 1000 * (1/2)^(9/T)

Dividing both sides by 1000:

0.125 = (1/2)^(9/T)

Taking the logarithm of both sides:

log(0.125) = (9/T) * log(1/2)

Simplifying:

log(0.125) = (-9/T) * log(2)

Solving for T:

T = -9 / (log(0.125) / log(2))

T ≈ 3 hours

Therefore, the answer is C: 3 hours.

A Radioactive Material Initially Is Observed to Have an Activity