## Problem Set 4

NOTE: You may have to look at the Nuclear Table or the Element Tables to answer some of the questions.

1) A certain isotope has a half-life of 20 years. If I had 2,000,000 of these nuclei in 1995, how many will I have in the year 2015? How many in 2035, 2055, 2075?
EXPLANATION

2) In a sample of radioactive waste there are 4 kg of 137Cs. How much is there after 30 years has elapsed? after 60 years?
EXPLANATION

3) Write the equations that describe a series of beta decays, leading from 90Br to 90Sr. .
EXPLANATION

4) The half-life of 14C is about 6000 years. Living things are made of carbon, and a small fraction of that carbon is 14C. Suppose that in the shinbone of a living human being I ordinarily find 8 micrograms of 14C. Now I find a fossil of an ancient human, and in the shinbone there are 4 micrograms of this isotope. When did this human being live?

(The assumption here is that a living thing is built out of carbon from the environment, and keeps building itself as long as it is alive. Therefore it always has the same fraction of 14C in its body as there is in the carbon of the environment. But when it dies it stops taking anything in from the environment -- such as nutrients -- and whatever radioactive carbon it has decays.)
EXPLANATION

5) If I find a shinbone with 1 microgram of 14C, how long ago did that human live?
EXPLANATION

6) Write the equation for the beta decay of neptunium-239.