Chapter 12 Quiz — Radioactivity Fundamentals

Instructions: Select the best answer for each question. Each question has exactly one correct answer.

Q1. The fundamental assumption of the radioactive decay law is that each nucleus:

(a) Decays after a predetermined time set at its creation (b) Has a constant probability $\lambda \, dt$ of decaying in time $dt$, independent of its age (c) Decays when it accumulates enough thermal energy to overcome the potential barrier (d) Has a probability of decaying that increases linearly with time

Q2. A sample initially contains $N_0$ radioactive atoms. After exactly 4 half-lives, how many atoms remain undecayed?

(a) $N_0 / 4$ (b) $N_0 / 8$ (c) $N_0 / 16$ (d) $N_0 / 32$

Q3. The mean life $\tau$ of a radioactive isotope is related to its half-life $t_{1/2}$ by:

(a) $\tau = t_{1/2}$ (b) $\tau = t_{1/2} / 2$ (c) $\tau = t_{1/2} / \ln 2 \approx 1.443 \, t_{1/2}$ (d) $\tau = t_{1/2} \times \ln 2 \approx 0.693 \, t_{1/2}$

Q4. One curie (Ci) is defined as:

(a) The activity of 1 gram of $^{238}$U (b) $3.7 \times 10^{10}$ decays per second (c) 1 decay per second (d) The activity that delivers 1 rad of dose per hour

Q5. Which isotope has the highest specific activity (activity per gram)?

(a) $^{238}$U ($t_{1/2} = 4.468 \times 10^9$ yr) (b) $^{226}$Ra ($t_{1/2} = 1600$ yr) (c) $^{60}$Co ($t_{1/2} = 5.271$ yr) (d) $^{3}$H ($t_{1/2} = 12.32$ yr)

Q6. In a two-member decay chain (parent $\to$ daughter $\to$ stable), secular equilibrium occurs when:

(a) The parent half-life is much shorter than the daughter half-life (b) The parent and daughter half-lives are equal (c) The parent half-life is much longer than the daughter half-life (d) Both parent and daughter are stable

Q7. At secular equilibrium in a decay chain, which statement is true?

(a) All members have the same number of atoms $N$ (b) All members have the same activity $A$ (c) All members have the same decay constant $\lambda$ (d) All members have the same half-life

Q8. In the transient equilibrium regime, the daughter activity is:

(a) Less than the parent activity (b) Equal to the parent activity (c) Greater than the parent activity, and both decay at the parent's rate (d) Greater than the parent activity, and both decay at the daughter's rate

Q9. If $^{212}$Bi can decay by $\alpha$ (36%) or $\beta^-$ (64%), and its total half-life is 60.55 min, what is the partial half-life for $\alpha$ decay?

(a) 21.8 min (b) 38.8 min (c) 60.55 min (d) 168 min

Q10. In carbon-14 dating, the "clock starts" when:

(a) The $^{14}$C atom is produced in the atmosphere (b) The organism dies and stops exchanging carbon with the environment (c) The sample is placed in the detector (d) The $^{14}$C/$^{12}$C ratio reaches $1.2 \times 10^{-12}$

Q11. The practical age range of $^{14}$C dating is approximately:

(a) 10 to 1,000 years (b) 300 to 50,000 years (c) 100,000 to 1 million years (d) 1 million to 4.5 billion years

Q12. In U-Pb dating, the concordia diagram plots:

(a) $^{206}$Pb/$^{238}$U vs. $^{207}$Pb/$^{235}$U, with concordant ages falling on a curve (b) $^{238}$U/$^{206}$Pb vs. time (c) Total lead content vs. total uranium content (d) $^{206}$Pb/$^{204}$Pb vs. $^{207}$Pb/$^{204}$Pb

Q13. The four natural radioactive series are classified by $A \bmod 4$ because:

(a) Proton number changes by 4 in each decay (b) $\alpha$ decay changes $A$ by 4, and $\beta$ decay does not change $A$ (c) There are four types of radioactive decay (d) Neutron number is always divisible by 4 in heavy nuclei

Q14. The neptunium series ($4n+1$) is "extinct" because:

(a) $^{237}$Np is too stable to decay (b) The series never existed in nature (c) The parent $^{237}$Np ($t_{1/2} = 2.14 \times 10^6$ yr) has decayed away over the 4.6 Gyr age of the Solar System (d) Neptunium-237 was only created in nuclear reactors

Q15. $^{99\text{m}}$Tc ($t_{1/2} = 6.006$ h) is the most widely used radioisotope in nuclear medicine. A hospital receives a 20 mCi source at 8:00 AM. The activity at 2:00 PM the same day is approximately:

(a) 20 mCi (b) 15 mCi (c) 10 mCi (d) 5 mCi

Q16. A sample of pure $^{226}$Ra is sealed in a container. After 30 days, the $^{222}$Rn activity will be approximately:

(a) Zero — radon has not had time to form (b) About 50% of the radium activity (c) Approximately equal to the radium activity (d) Much greater than the radium activity

Q17. The Rb-Sr isochron method eliminates the problem of unknown initial daughter content by:

(a) Assuming all initial $^{87}$Sr has decayed (b) Measuring multiple cogenetic samples with different Rb/Sr ratios and fitting a line (c) Using a standard with known $^{87}$Sr content (d) Only analyzing samples with zero initial strontium

Q18. The Bateman equations describe:

(a) The probability of nuclear fission (b) The populations of members in a radioactive decay chain as functions of time (c) The binding energy as a function of mass number (d) The angular distribution of emitted radiation

Answer Key