Question

You are using a Geiger counter to measure the activity of a radioactive substance over the course of several minutes. If the reading of 400. counts has diminished to 100. counts after 54.3 minutes , what is the half-life of this substance?

Express your answer with the appropriate units.

t1/2 =

27.2 min

Correct

Part B

An unknown radioactive substance has a half-life of 3.20 hours . If 20.6 g of the substance is currently present, what mass A0 was present 8.00 hours ago?

Express your answer with the appropriate units.

A0 =

Part C

Americium-241 is used in some smoke detectors. It is an alpha emitter with a half-life of 432 years. How long will it take in years for 45.0 % of an Am-241 sample to decay?

Express your answer with the appropriate units.

t =

Part D

A fossil was analyzed and determined to have a carbon-14 level that is 80 % that of living organisms. The half-life of C-14 is 5730 years. How old is the fossil?

Express your answer with the appropriate units.

t =

Answer 1

B) rate constant,k = ln2/t_1/2 = 0.693/3.2 = 0.217 hr^-1

Now, the governing equation for 1st order kinetics is :-

k*t = ln{[A₀]/[A]}

or, 0.217*8 = ln{[A₀]/20.6}

or, [A₀] = 116.53 g

C) rate constant,k = ln2/t_1/2 = 0.693/432 = 1.605*10^-3 yr^-1

Now, the governing equation for 1st order kinetics is :-

k*t = ln{[A₀]/[A]}

or, 1.605*10^-3*t = ln(100/55)

or, time ,t = 372.48 years.

D) rate constant,k = ln2/t_1/2 = 0.693/5730 = 1.21*10^-4 yr^-1

Now, the governing equation for 1st order kinetics is :-

k*t = ln{[A₀]/[A]}

or, 1.21*10^-4*t = ln(100/80)

or, time ,t = 1844.46 years.