Chapter 9, Problem Set 1

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```					Chapter 21, Problem Set 1                                                              Name_______
AP Chemistry—Spontaneous Nuclear Reactions

1. Complete this table of characteristics of common radioactive “rays”.
Name       Charge Mass (amu) Symbol & description                                         Penetrating ability
Alpha, 

Beta, 

Gamma, 

Positron, +

2. In a nuclear equation, what two sums must be equal on both sides of the arrow? What
do these sums represent?

Example: Sodium-24 is an unstable isotope that decays by beta emission (or beta decay).
Write the nuclear equation for this dacay.
Answer: 2411Na  0-1e + 2412Mg

3. Write nuclear equations representing each of these nuclear reactions.

a. beta emission of boron-12

b. alpha decay of californium-244

c. positron emission of an antimony isotope, producing tin-120

g. positron decay of sulfur-31

h. alpha decay of uranium-238

i. beta emission of thorium-234

j. a three step decay by actinium-228, first by beta emission,
then an alpha decay, then another alpha decay.
Selected Answers: 2. Mass numbers and atomic numbers, representing no change in either the total
number of nuclear particles or the total charge. 3. a. 125B  0-1e + 126C b. 24498Cf  42He + 24096Cm
c. 51Sb  +1e + 50Sn
120      0      120
d. 82Pb  -1e + 83Bi
214         0     214
Chapter 9, Problem Set 2 AP Chem                                 Name___________________
Half-life Problems

Use “half-life analysis” to solve these problems.

1. Silicon-20 undergoes beta decay, with a half-life of 6.0 hours. (a) What fraction of the
original sample will remain unchanged after one day (24 hours)? (b) What isotope is the
product of the nuclear decay?

2. A 120.0g sample of a radioactive isotope undergoes beta decay, such that after 81
days only 15.0g remain of the original isotope. (a) If the product of the decay is
uranium-233, what is the original isotope? (b) What is the half-life of the original
isotope?

3. Carbon-14 has a half-life of 5730 years, decaying by beta emission. Freshly cut wood
emits 15.2 beta particles per minute per gram of carbon. After 5730 years, half of the
carbon-14 in the wood will have decayed, and it will be emitting only half as many beta
particles per minute per gram. Suppose you measure the amount of beta radiation from
an ax handle found at an archeological dig, and determine that it emits 3.8 beta particles
per minute per gram of carbon. (a) How old is the ax? (b) What is the decay product?

4. A 40.0 mg sample of phosphorus-33 beta decays to a stable isotope, with only 10.0
mg remaining of phosphorus-33 after 50.0 days. a) What is the half-life of 33P? b) How
much of what other isotope is present after 50.0 days?

5. The strontium-90, one of the products of uranium fission, has a half-life of 28 years.
Suppose 1.0g is all the strontium-90 that remains in a sample after 112 years. (a) What
mass of strontium-90 was originally in the sample? (b) If strontium-90 decays by beta
emission, and this decay product also undergoes beta decay with a half-life of only 64
hours, what mass of what new isotope remains in the sample after 112 years?

6. Sodium-24 decays by beta emission with a half-life of 15 hours. (a) What fraction of
a 1.66g sample of sodium-24 will remain unchanged after 45 hours? (b) What mass of
sodium-24 will remain?

Answers: 1. a) 1/16 b) 20P 2. a) 233Pa b) 27.0 days 3. a) approx 11000 years (rounded from 11460)
b) 14N 4. a) 25 d b) 30.0 mg 33S 5. a) 16 g b) 15 g of 90Zr 6. a) 1/8 b) 0.21 g

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