Q: Which of the following nuclear reactions represents beta minus ($$\beta^-) $$decay?

$$^{A}_{Z}X \$$rightarrow ^{A}$$_{Z+1}Y + e^- + \text{energy}$$

Q: A sample of $$^{18}\mathrm{F} ($$half-life 110 min) is used for PET imaging. If $$3.2 \times 10$$^{10}$$ nuclei remain after 24 hours, how many nuclei were present initially? (Use N(t$$) = $$N_0$$ $$(1/2)^{t/t_{1/2}$$}$$)

$$N_0 = 3.2$$ \times $$10^{10}$$ \times $$2^{24\times 60/110}$$

Question 1

Which of the following statements best describes the difference between the strong nuclear force and the electromagnetic force within an atomic nucleus?

Accepted Answer

The strong force is an attractive force between all nucleons and is stronger than the electromagnetic force at nuclear distances.

Question 2

A nucleus of $$^{238}\mathrm{U} ($$uranium-238) has an atomic number $$Z = 92. $$How many neutrons does it contain?

Accepted Answer

$$146$$

Question 3

Which equation correctly expresses the exponential decay of the number of radioactive nuclei $$N(t)$$ over time?

Accepted Answer

$$N(t) = N_0$ e$$^{-rt}$$

Question 4

The half-life $$t_{1/2} of a $$radioactive isotope is related to its mean lifetime $$	au by $$which equation?

Accepted Answer

$$t_{1/2} = 	au \ln(2)$$

Question 5

If a radioactive sample has a half-life of 3 hours, what fraction of the original nuclei remains after 9 hours?

Accepted Answer

$$1/8$$

Question 6

Which of the following nuclear reactions represents beta minus ($$\beta^-) $$decay?

Accepted Answer

$$^{A}_{Z}X \$$rightarrow ^{A}$$_{Z+1}Y + e^- + 	ext{energy}$$

Question 7

The binding energy per nucleon for $$^{204}\mathrm{Pb} is $$approximately $$7.88$$ MeV. What does this value represent?

Accepted Answer

The average energy needed to separate each nucleon from the nucleus.

Question 8

Which of the following best explains why heavy nuclei (A \u003e 60) can release energy by fission?

Accepted Answer

Their binding energy per nucleon increases when they split into smaller nuclei.

Question 9

A radioactive sample has an initial activity $$R_0. $$What is the activity $$R$$ after a time $$t$$?

Accepted Answer

$$R = R_0$ e$$^{-t/	au}$$

Question 10

Which type of radiation is most likely to cause the greatest biological damage if ingested, assuming equal absorbed doses?

Accepted Answer

Alpha particles

Question 11

A sample of $$^{18}\mathrm{F} ($$half-life 110 min) is used for PET imaging. If $$3.2 	imes 10$$^{10}$$ nuclei remain after 24 hours, how many nuclei were present initially? (Use N(t$$) = $$N_0$$ $$(1/2)^{t/t_{1/2}$$}$$)

Accepted Answer

$$N_0 = 3.2$$ 	imes $$10^{10}$$ 	imes $$2^{24	imes 60/110}$$

Question 12

Which of the following is the correct formula for the radius $$R of a $$nucleus with mass number $$A$$?

Accepted Answer

$$R = r_0$ A$$^{1/3}$$

Question 13

Which of the following statements about isotopes is correct?

Accepted Answer

Isotopes of an element have the same number of protons but different numbers of neutrons.

Question 14

Which of the following best describes the process of radioactive dating using $$^{14}\mathrm{C}$$?

Accepted Answer

Measuring the ratio of $$^{14}\mathrm{C} to$$ $$^{12}\mathrm{C} in a $$sample to estimate its age.

Question 15

Which of the following nuclear decay processes does NOT change the atomic number $$Z of $$the nucleus?

Accepted Answer

Gamma decay

Question 16

The SI unit for absorbed dose of ionizing radiation is the gray (Gy). What does 1 Gy represent?

Accepted Answer

1 J of energy absorbed per kilogram of tissue

Question 17

A $$^{11}\mathrm{C}$$ nucleus (Z = 6) decays to $$^{11}\mathrm{B} (Z = 5). $$What type of decay has occurred?

Accepted Answer

Beta plus decay

Question 18

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

Accepted Answer

Ionizing radiation can cause mutations in DNA, which may lead to cancer.

Question 19

Which of the following best explains why neutrons are needed in the nucleus for stability, especially in heavier elements?

Accepted Answer

Neutrons provide additional strong force attraction without increasing electromagnetic repulsion.

Question 20

Which of the following is the correct formula for the total nuclear binding energy $$B of a $$nucleus?

Accepted Answer

$$B = (Z m_H + N m_n - m_{atom}) 	imes 931.49\ \mathrm{MeV/u}$$

Nuclear Physics: Structure, Stability, Binding Energy, and Radioactivity

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