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?
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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?
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3) Write the equations that describe a series of beta decays, leading from ⁹⁰Br to ⁹⁰Sr. .
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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.)
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5) If I find a shinbone with 1 microgram of ¹⁴C, how long ago did that human live?
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6) Write the equation for the beta decay of neptunium-239.
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7) Write the equation for alpha decay of ²⁵⁴₁₀₀Fm.
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8) Write the equation for beta decay of carbon-14.
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9) Write the equation for alpha decay of polonium-210.
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