Question

11)

Part A

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 70.8 minutes , what is the half-life of this substance?

Express your answer with the appropriate units.

t1/2 =

Part B

An unknown radioactive substance has a half-life of 3.20 hours . If 24.2 gof 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 33.0 % 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 60 % 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.

Answer 1

part A )

for first order reaction :

k = 1/t * ln (Ao / At)

k = 1/ 70.8 * ln (400 / 100)

k = 0.0196 min-1

half life = 0.693 / k

             = 0.693 / 0.0196

            = 35.4 min

half-life = 35.4 min

Part B

rate constant = k = 0.693 / 3.20 = 0.217 hour-1

k = 1/t * ln (Ao / At)

0.217 = 1 / 8 * ln (Ao / 24.2)

ln (Ao / 24.2) = 1.7325

Ao = 138.8 g

Ao = 139 g

part C)

k = 0.693 / 432 = 1.60 x 10^-3 year-1

Ao = 100

At = 100 -33 = 67

t = 1/1.60 x 10^-3 * ln (100 / 67)

t = 250 years

Part D

rate constant = k = 0.693 / 5730 = 1.21 x 10^-4

t = 4222 years