A radioactive material initially is observed to have an activity of 1 600 decays/s.If six hours later it is observed to have an activity of 400 decays/s,what is its half-life?
A)six hours
B)three hours
C)twelve hours
D)seven hours
E)not enough information

Question

A radioactive material initially is observed to have an activity of 1 600 decays/s.If six hours later it is observed to have an activity of 400 decays/s,what is its half-life?
A)six hours
B)three hours
C)twelve hours
D)seven hours
E)​not enough information

Quizplus · Accepted Answer

The half-life of a radioactive material is defined as the time it takes for half of the substance to decay. We can use the formula:

A = A₀(1/2)^(t/T)

where A is the final activity, A₀ is the initial activity, t is the time that has passed, and T is the half-life.

Plugging in the values given in the problem, we get:

400 = 1600(1/2)^(6/T)

Simplifying, we can divide both sides by 1600 to get:

1/4 = (1/2)^(6/T)

Taking the logarithm of both sides, we get:

log(1/4) = log[(1/2)^(6/T)]

Using logarithm rules, we can bring the exponent down:

log(1/4) = (6/T)log(1/2)

Simplifying, we get:

log(1/4) = (-6/T)

Using a calculator, we can solve for T:

T = -6/log(1/4) = 3.0 hours

Therefore, the half-life of the radioactive material is 3.0 hours, which corresponds to answer choice B.

A Radioactive Material Initially Is Observed to Have an Activity