Chapter 11 Quiz: Superheavy Elements

Instructions: Select the best answer for each question. Answers are provided at the end.

Q1. Without shell corrections, the liquid drop model predicts that nuclei beyond approximately what proton number would have zero fission barrier and fission instantaneously?

(a) Z $\approx$ 82 (b) Z $\approx$ 92 (c) Z $\approx$ 104 (d) Z $\approx$ 114 (e) Z $\approx$ 126

Q2. The Strutinsky shell correction method calculates $\delta E_{\text{shell}}$ as the difference between:

(a) The total nuclear binding energy and the Coulomb energy (b) The sum of occupied single-particle energies and the integral of the smoothed level density (c) The fission barrier height and the neutron separation energy (d) The proton and neutron Fermi energies

Q3. In cold fusion synthesis of superheavy elements, the target nucleus is typically:

(a) $^{48}$Ca (b) $^{208}$Pb or $^{209}$Bi (c) An actinide (U, Pu, Cm, etc.) (d) A medium-mass nucleus ($^{50}$Ti, $^{54}$Cr, etc.)

Q4. The advantage of cold fusion over hot fusion is that the compound nucleus:

(a) Has a larger fission barrier (b) Is more neutron-rich (c) Is formed with lower excitation energy, requiring evaporation of fewer neutrons (d) Has a larger production cross section for Z > 112

Q5. Calcium-48 is particularly effective as a projectile for hot fusion because (choose all that apply):

I. It is doubly magic (Z = 20, N = 28) II. It has a large neutron excess (N/Z = 1.4) III. It is the lightest projectile that can reach Z > 112 with actinide targets IV. Its doubly magic structure enhances the fusion probability

(a) I and II only (b) I, II, and IV only (c) I, II, III, and IV (d) II and III only

Q6. The production cross section for element 112 at GSI via cold fusion was approximately:

(a) 1 millibarn (b) 1 microbarn (c) 1 nanobarn (d) 1 picobarn (e) 1 femtobarn

Q7. Which element was the first to be discovered in Asia, and at which laboratory?

(a) Flerovium (Fl, Z = 114), at the Institute of Modern Physics in Lanzhou (b) Nihonium (Nh, Z = 113), at RIKEN in Japan (c) Moscovium (Mc, Z = 115), at JINR in Dubna (d) Oganesson (Og, Z = 118), at RIKEN in Japan

Q8. The target material used for the synthesis of element 117 (tennessine) was:

(a) $^{248}$Cm, produced at ORNL (b) $^{249}$Bk, produced at ORNL with a half-life of 330 days (c) $^{249}$Cf, produced at JINR (d) $^{244}$Pu, available commercially

Q9. The 1s electron in oganesson (Z = 118) travels at approximately what fraction of the speed of light?

(a) 0.10c (b) 0.43c (c) 0.65c (d) 0.86c (e) 0.99c

Q10. Which of the following is a predicted property of oganesson that differs from typical noble gas behavior?

(a) It is predicted to be a solid at room temperature (b) It is predicted to have a positive electron affinity (c) It may be a semiconductor rather than an insulator (d) All of the above

Q11. The center of the island of stability is predicted to occur at approximately:

(a) Z = 82, N = 126 (b) Z = 100, N = 152 (c) Z = 114 or 120, N = 184 (d) Z = 126, N = 184 (e) Z = 114, N = 164

Q12. The most neutron-rich superheavy isotope produced to date has a neutron number of approximately:

(a) N = 162 (b) N = 170 (c) N = 176 (d) N = 184 (e) N = 190

Q13. In the factored cross section $\sigma_{\text{SHE}} = \sigma_{\text{capture}} \times P_{\text{fusion}} \times P_{\text{survival}}$, which factor is primarily responsible for the extremely small overall cross sections?

(a) $\sigma_{\text{capture}}$ — the Coulomb barrier is too high (b) $P_{\text{fusion}}$ — most captured systems undergo quasi-fission (c) $P_{\text{survival}}$ — the compound nucleus usually fissions before cooling (d) Both $P_{\text{fusion}}$ and $P_{\text{survival}}$ — each is of order $10^{-3}$ or less

Q14. The direct relativistic effect on atomic orbitals causes:

(a) s and p$_{1/2}$ orbitals to expand; d and f orbitals to contract (b) s and p$_{1/2}$ orbitals to contract; d and f orbitals to expand (via indirect effect) (c) All orbitals to contract uniformly (d) All orbitals to expand uniformly

Q15. Element 118 is named oganesson after Yuri Oganessian. What is distinctive about this naming?

(a) It was the first element named after a city (b) It was only the second element named after a living person (c) It was the first element named by the IUPAC (d) It was named posthumously after Oganessian passed away

Q16. Which of the following is NOT a candidate reaction for producing element 120?

(a) $^{54}$Cr + $^{248}$Cm (b) $^{50}$Ti + $^{249}$Cf (c) $^{48}$Ca + $^{252}$Cf (d) $^{58}$Fe + $^{244}$Pu

Q17. The SHE Factory at JINR in Dubna features:

(a) The DC-280 cyclotron with 5-10 times higher beam intensity than the U400 (b) A free-electron laser for superheavy element spectroscopy (c) A radioactive beam facility using in-flight fragmentation (d) A synchrotron capable of accelerating $^{208}$Pb to relativistic energies

Q18. The half-lives of known flerovium isotopes increase with increasing neutron number. The most natural explanation for this trend is:

(a) Heavier isotopes have smaller Q-values for alpha decay (b) Heavier isotopes are closer to the N = 184 shell closure, which increases the fission barrier (c) The liquid drop model predicts longer half-lives for more neutron-rich nuclei (d) Both (a) and (b) contribute

Answer Key

  1. (c) Z $\approx$ 104. The liquid drop fission barrier vanishes near Z = 104-106 without shell corrections.

  2. (b) The Strutinsky method defines $\delta E_{\text{shell}}$ as the difference between the sum of occupied single-particle energies and the corresponding integral of the smoothed (averaged) level density.

  3. (b) Cold fusion uses $^{208}$Pb or $^{209}$Bi as targets. Their doubly magic (or near-magic) structure minimizes the excitation energy of the compound nucleus.

  4. (c) The lower excitation energy in cold fusion means only 1 neutron must be evaporated (1n channel), dramatically increasing the survival probability.

  5. (b) I, II, and IV. Statement III is incorrect — lighter projectiles could reach Z > 112 with very heavy targets, but $^{48}$Ca is optimal due to its magic structure and neutron richness.

  6. (d) 1 picobarn ($10^{-36}$ cm$^2$). This is one of the smallest cross sections ever measured in nuclear physics.

  7. (b) Nihonium (Nh, Z = 113) was discovered at RIKEN in Wako, Japan — the first element discovered in Asia.

  8. (b) $^{249}$Bk, with a half-life of 330 days, was produced by extended irradiation at ORNL's High Flux Isotope Reactor.

  9. (d) $v_{1s}/c \approx Z/137 = 118/137 \approx 0.86$.

  10. (d) All three predictions have been made for oganesson based on relativistic calculations.

  11. (c) Z = 114 (macroscopic-microscopic models) or Z = 120 (relativistic mean-field models), with N = 184 predicted by essentially all models.

  12. (c) N = 176, for $^{294}$Og. The N = 184 closure has not been reached.

  13. (d) Both $P_{\text{fusion}}$ and $P_{\text{survival}}$ are very small. The capture cross section is on the order of millibarns (relatively large), but the fusion and survival probabilities each contribute factors of $\sim 10^{-3}$ or less, making the overall cross section picobarn-scale.

  14. (b) The direct effect contracts s and p$_{1/2}$ orbitals; the indirect effect (enhanced screening by contracted inner orbitals) causes d and f orbitals to expand.

  15. (b) Oganesson was only the second element named after a living person. The first was seaborgium (Z = 106), named for Glenn Seaborg.

  16. (c) $^{48}$Ca + $^{252}$Cf $\rightarrow$ Z = 118 (oganesson), not Z = 120. Reaching Z = 120 with $^{48}$Ca would require a target beyond $^{252}$Cf (e.g., einsteinium or fermium), which are impractical.

  17. (a) The DC-280 cyclotron, operational since 2020, delivers beam intensities 5-10 times greater than the U400 used for elements 113-118.

  18. (d) Both effects contribute. More neutron-rich isotopes have smaller Q$_\alpha$ values (increasing the alpha-decay half-life via the Gamow tunneling factor) and are closer to the N = 184 shell closure (increasing the fission barrier and thus the SF half-life).