a) You are using a Geiger counter to measure the activity of a radioactive subst

Question

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

b)An unknown radioactive substance has a half-life of 3.20 hours . If 14.6 g of the substance is currently present, what mass A0 was present 8.00 hours ago?

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 30.0 % of an Am-241 sample to decay?

d) A fossil was analyzed and determined to have a carbon-14 level that is 50 % that of living organisms. The half-life of C-14 is 5730 years. How old is the fossil?

Explanation / Answer

a. with calculation

A = Ao e-0.693t/t1/2

100 = 400 xe-0.693x76.2/t1/2

ln0.25 = - 52.8/t1/2

t1/2 = (-52.8) / (-1.386) = 38.1 min

answer without calculation based on the observation that A = Ao/4.

That means that 76.2 minutes = 2 t1/2 . Thus t1/2 = 76.2/2 = 38.1 min.

b.

m = mo e-0.693t/t1/2

14.6 = moe-0.693x8/3.2             

Ln14.6 -lnmo = - 1.7325

2.68 + 1.73 = lnmo

mo = 82.3 g

c.

ln (A/Ao) = -0.693t/t1/2

ln 0.30 = -0.693t/432

t= 750 years

d.

5730 years (observe that carbon level is ½ that of living organism. The living organism provides the initial C14 quantity)

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.