Question

In 2010, a team of scientists from Russia and the United States reported creation of the first atom of element 117, which is named tennessine, and whose symbol is Ts. The synthesis involved the collision of a target of \(_{97}^{249} \mathrm{Bk}\) with accelerated ions of an isotope which we will denote Q. The product atom, which we will call Z, immediately releases neutrons and forms \(_{97}^{249} \mathrm{Bk} :\) $$_{97}^{249} \mathrm{Bk}+\mathrm{Q} \longrightarrow \mathrm{Z} \longrightarrow_{117 \mathrm{Ts}}^{294 \mathrm{Ts}}+3_{0}^{1} \mathrm{n}$$ (a) What are the identities of isotopes Q and Z? (b) Isotope Q is unusual in that it is very long-lived (its half-life is on the order of 1019 yr) in spite of having an unfavorable neutron-to-proton ratio (Figure 21.1). Can you propose a reason for its unusual stability? (c) Collision of ions of isotope Q with a target was also used to produce the first atoms of livermorium, Lv. The initial product of this collision was \(_{116}^{296} \mathrm{Zn}\). What was the target isotope with which Q collided in this experiment?

Short answer

(a) The identities of isotopes Q and Z are \(_{20}^{45}\mathrm{Ca}\) (Calcium) and \(_{117}^{297}\), respectively. (b) The unusual stability of isotope \(_{20}^{45}\mathrm{Ca}\) could be attributed to the "magic number" of nucleons, in this case, having a magic number of protons (20) which leads to a closed shell of protons. (c) The target isotope with which Q collided in the experiment to produce livermorium is \(_{96}^{251}\mathrm{Cm}\) (Curium).

Step-by-step solution

(a) Identities of isotopes Q and Z

Given the nuclear reaction: \[_{97}^{249} \mathrm{Bk}+\mathrm{Q} \longrightarrow \mathrm{Z} \longrightarrow_{117}^{294}\mathrm{Ts}+3_{0}^{1}\mathrm{n} \] We need to find the identities of the isotopes Q and Z. First of all, we will find the atomic number and mass number of isotope Q as follows: Let isotope Q have atomic number \(x\) and mass number \(y\). The conservation of atomic numbers (\(Z\)) and mass numbers (\(A\)) in a nuclear reaction implies: \(x + 97 = 117\) and \(y + 249 = 294\) On solving these equations, we get: \(x=20\) and \(y=45\) The identity of isotope Q is then \(_{20}^{45}\mathrm{Ca}\) (Calcium). Next, let's find the atomic number and mass number of isotope Z. Since Z immediately decays and releases 3 neutrons to form Tennessine, its atomic number remains 117 and the mass number becomes 297 (294 + 3 = 297). The identity of isotope Z is: \(_{117}^{297}\)

(b) Stability of isotope Q

Isotope \(_{20}^{45}\mathrm{Ca}\) has an unusually long half-life of around \(10^{19}\) years, despite its unfavorable neutron-to-proton ratio. A possible explanation for its unusual stability could be the "magic number" of nucleons (protons and neutrons). Magic numbers are the numbers of nucleons that fill energy shells in the nucleus, and when a nucleus has a magic number of any type of nucleons, it usually has a higher stability than its close neighbors. In this case, the isotope could have a magic number of protons, neutrons, or both. The atomic number of Calcium is 20, which is a magic number for protons. This suggests that the stability of the isotope comes from having a closed shell of protons.

(c) Target isotope for livermorium production

To produce the first atoms of livermorium, Lv, the same ions of isotope Q were used. The experiment resulted in the initial product \(_{116}^{296}\mathrm{Zn}\). Let the target isotope have atomic number \(p\) and mass number \(q\). Using the conservation of atomic numbers (Z) and mass numbers (A) in a nuclear reaction, we can write: \(20 + p = 116\) and \(45 + q = 296\) On solving these equations, we get: \(p = 96\) and \(q = 251\) The target isotope with which Q collided in this experiment is \(_{96}^{251}\mathrm{Cm}\) (Curium).

Key concepts

Isotope Identification

Understanding isotopes is essential in the field of nuclear chemistry. An isotope is an atom of the same element that contains the same number of protons but different numbers of neutrons in its nucleus. These varying numbers of neutrons contribute to differences in atomic mass but not the chemical properties of the element. Isotope identification is a foundational skill in nuclear chemistry which involves determining the identity of an atom based on its proton (atomic) number and neutron number. Typically, isotopes are represented with the notation eqn, where neqn is the symbol for the element, neqn represents the atomic mass number (total number of protons and neutrons), and neqn is the atomic number (number of protons).

For example, in the nuclear reaction given in the exercise, the isotope eqn reacts with a target isotope to form a new isotope eqn, which then releases neutrons to become Tennessine (eqn). By using the law of conservation of mass and the conservation of charge, which apply to all nuclear reactions, we can determine the identity of isotopes involved in the reaction. The conservation laws ensure that both the atomic number and the mass number are conserved across the nuclear reaction, helping us pinpoint the exact isotopes in question.

Neutron-to-Proton Ratio

The neutron-to-proton ratio, often symbolized as n/p, is crucial for understanding the stability of a nucleus. Atoms are most stable when they have a certain ratio of neutrons to protons, which varies depending on the size of the nucleus. If the ratio is too high or too low, the nucleus becomes unstable and is prone to decay. Isotopes with unfavorable n/p ratios tend to have shorter half-lives and are usually radioactive.

However, some isotopes, like eqn from the provided exercise, defy this expectation by exhibiting unusually long half-lives despite having an unfavorable neutron-to-proton ratio. This implies the presence of additional factors contributing to nuclear stability. One such factor could be the concept of 'magic numbers', which refer to the idea that shells within the nucleus, much like the electron shells in an atom, can fill up and provide extra stability. The presence of a closed shell can significantly increase an isotope's stability, thus making it an exception to the typical trends of the n/p ratio.

Nucleon Magic Numbers

The term 'nucleon magic numbers' refers to specific numbers of protons or neutrons in a nucleus that create a highly stable configuration. These numbers are akin to the noble gases in the periodic table, which are particularly stable due to their filled electron shells. Similarly, when a nucleus has a complete shell of protons or neutrons, it attains an exceptional stability. These 'magic numbers' are 2, 8, 20, 28, 50, 82, and 126 for protons and neutrons, and possessing one of these numbers tends to make an isotope more resistant to radioactive decay.

In our exercise, isotope eqn is unusually stable, with an incredibly long half-life despite an unfavorable neutron-to-proton ratio. The atomic number 20 corresponds to one of these magic numbers, suggesting that this stability arises from having a closed proton shell. This principle helps explain why certain isotopes are more stable than others and demonstrates the significance of understanding nucleon magic numbers in predicting the stability of isotopes in nuclear chemistry.