Q: A rock contains a Pb-206 to U-238 mass ratio of 0.145 : 1.00. Assuming no initial Pb-206, what is the age of the rock? (Half-life of U-238 is $$4.5 \times 10^9$ years.)

Approximately $$6.6 \times 10^8$ years

Question 1

Which of the following statements best describes the difference between alpha, beta, and gamma radiation in terms of their ionizing and penetrating abilities?

Accepted Answer

Alpha particles are the most ionizing but least penetrating, beta particles are intermediate in both, and gamma rays are the least ionizing but most penetrating.

Question 2

Which nuclear equation correctly represents the alpha decay of $$^{216}_{84}\mathrm{Po}$$?

Accepted Answer

$$^{216}_{84}\mathrm{Po} \$$rightarrow ^{212}$$_{82}\mathrm{Pb} $$+ ^{4}$$_{2}\mathrm{He}$$

Question 3

A radioactive isotope has a half-life of 10 years. If you start with 80 grams, how much remains after 30 years?

Accepted Answer

10 grams

Question 4

Which of the following best explains why nuclei with a neutron-to-proton ratio (N/Z) that is too high tend to undergo beta decay?

Accepted Answer

Beta decay converts a neutron into a proton, lowering the N/Z ratio toward stability.

Question 5

Which of the following is a real-world application of radioisotopes in medicine?

Accepted Answer

Using $$^{18}\mathrm{F} in $$PET scans to monitor glucose metabolism in the brain

Question 6

A sample of $$^{14}\mathrm{C}$$ has a decay rate of 3.825 disintegrations per minute per gram of carbon. If the decay rate in living organisms is 15.3 dis/min·g C, what is the approximate age of the sample? (Half-life of $$^{14}\mathrm{C} is 5730 $$years.)

Accepted Answer

11,460 years

Question 7

Which of the following nuclear reactions is an example of positron emission?

Accepted Answer

$$^{22}_{11}\mathrm{Na} \$$rightarrow ^{22}$$_{10}\mathrm{Ne} $$+ ^{0}$$_{+1}\mathrm{e}$$

Question 8

Which of the following statements about nuclear fission and fusion is correct?

Accepted Answer

Fission involves the splitting of a large nucleus, while fusion involves the combining of small nuclei.

Question 9

A rock contains a Pb-206 to U-238 mass ratio of 0.145 : 1.00. Assuming no initial Pb-206, what is the age of the rock? (Half-life of U-238 is $$4.5 	imes 10^9$ years.)

Accepted Answer

Approximately $$6.6 	imes 10^8$ years

Question 10

Which of the following best describes the concept of mass defect in nuclear chemistry?

Accepted Answer

The difference in mass between the nucleus and the sum of the masses of its protons and neutrons, which is converted to binding energy.

Question 11

Which of the following is a correct statement about the biological effects of radiation?

Accepted Answer

The rem is a unit that accounts for both the energy absorbed and the biological effectiveness of the radiation.

Question 12

Which of the following nuclides is most likely to undergo positron emission based on its neutron-to-proton ratio?

Accepted Answer

$$^{22}_{12}\mathrm{Mg} (N/Z = 0.83)$$

Question 13

Which of the following best describes the function of control rods in a nuclear reactor?

Accepted Answer

They absorb excess neutrons to regulate the rate of the fission chain reaction.

Question 14

Which equation correctly relates the half-life ($$t_{1/2}) $$and the decay constant ($$k) $$for a first-order radioactive decay process?

Accepted Answer

$$t_{1/2} = \dfrac{0.693}{k}$$

Question 15

Which of the following is NOT a common use of radioactive isotopes?

Accepted Answer

Increasing the nutritional value of food

Question 16

Which of the following best explains why fusion reactions require extremely high temperatures to occur?

Accepted Answer

To provide enough energy to overcome the electrostatic repulsion between positively charged nuclei.

Question 17

Which of the following is a correct nuclear equation for the electron capture of $$^{76}_{36}\mathrm{Kr}$$?

Accepted Answer

$$^{76}_{36}\mathrm{Kr} $$+ ^{0}$$_{-1}\mathrm{e} \$$rightarrow ^{76}$$_{35}\mathrm{Br}$$

Question 18

Which of the following is a reason why there are no stable nuclei with atomic numbers greater than 83?

Accepted Answer

The strong nuclear force is not sufficient to overcome the electrostatic repulsion between the large number of protons.

Radioactivity and Nuclear Chemistry: Principles, Applications, and Calculations

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