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Ch.21 - Nuclear Chemistry
Brown - Chemistry: The Central Science 15th Edition
Brown15th EditionChemistry: The Central ScienceISBN: 9780137542970Not the one you use?Change textbook
All textbooksBrown 15th EditionCh.21 - Nuclear ChemistryProblem 74b
Chapter 21, Problem 74b

Chlorine has two stable nuclides, 35Cl and 37Cl. In contrast, 36Cl is a radioactive nuclide that decays by beta emission. (b) Based on the empirical rules about nuclear stability, explain why the nucleus of 36Cl is less stable than either 35Cl or 37Cl.

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1
Understand the concept of nuclear stability: Nuclear stability is influenced by the ratio of neutrons to protons in a nucleus. Stable nuclei tend to have a balanced ratio that falls within certain empirical rules.
Examine the neutron-to-proton ratio for each nuclide: Calculate the neutron-to-proton ratio for 35Cl, 36Cl, and 37Cl. For 35Cl, the number of neutrons is 18 (35 - 17 protons), and for 37Cl, it is 20 (37 - 17 protons). For 36Cl, the number of neutrons is 19 (36 - 17 protons).
Apply the empirical rules of nuclear stability: According to these rules, nuclei with a neutron-to-proton ratio close to 1:1 are generally more stable, especially for lighter elements like chlorine. Both 35Cl and 37Cl have ratios that are closer to this ideal compared to 36Cl.
Consider the role of magic numbers: Magic numbers are specific numbers of nucleons (either protons or neutrons) that confer extra stability to nuclei. Neither 35Cl nor 37Cl has a magic number of neutrons, but their ratios are more favorable compared to 36Cl.
Analyze the decay process: 36Cl undergoes beta decay, which is a process that occurs in unstable nuclei to achieve a more stable configuration. This indicates that 36Cl's neutron-to-proton ratio is not optimal, leading to its instability compared to 35Cl and 37Cl.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Nuclear Stability

Nuclear stability refers to the ability of a nucleus to remain intact without undergoing radioactive decay. Stable nuclides, like 35Cl and 37Cl, have a balanced ratio of protons to neutrons, which minimizes repulsive forces between protons and maximizes the strong nuclear force that holds the nucleus together. In contrast, unstable nuclides, such as 36Cl, have an unfavorable proton-to-neutron ratio, leading to instability and decay.
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Beta Decay

Beta decay is a type of radioactive decay in which a neutron in the nucleus is transformed into a proton, emitting a beta particle (an electron) and an antineutrino. This process increases the atomic number of the element while keeping the mass number constant, often resulting in a more stable configuration. The occurrence of beta decay in 36Cl indicates that its nuclear structure is not stable enough to maintain its current composition.
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Empirical Rules of Nuclear Stability

Empirical rules of nuclear stability, such as the 'belt of stability,' describe the relationship between the number of protons and neutrons in stable nuclei. Generally, stable nuclei have a neutron-to-proton ratio close to 1:1 for lighter elements, while heavier elements require more neutrons to offset the increased repulsion among protons. 36Cl's neutron-to-proton ratio deviates from these optimal ranges, contributing to its instability and propensity for beta decay.
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Related Practice
Textbook Question

Each of the following transmutations produces a radionuclide used in positron emission tomography (PET).

(a) In equations (i) and (ii), identify the species signified as 'X.'

(i) 14N(p,α)X

(ii) 18O(p,X)18F

(iii) 14N(d,n)15O

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Textbook Question

The table provided gives the number of protons (p) and neutrons (n) for four isotopes, identified only as (i)–(iv). a. Write the symbol for each of the isotopes.

Textbook Question

Radon-222 decays to a stable nucleus by a series of three alpha emissions and two beta emissions. What is the stable nucleus that is formed?

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Textbook Question

A laboratory rat is exposed to an alpha-radiation source whose activity is 14.3 mCi. (b) The rat has a mass of 385 g and is exposed to the radiation for 14.0 s, absorbing 35% of the emitted alpha particles, each having an energy of 9.12 * 10-13 J. Calculate the absorbed dose in millirads and grays.

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Textbook Question

Nuclear scientists have synthesized approximately 1600 nuclei not known in nature. More might be discovered with heavy-ion bombardment using high-energy particle accelerators. Complete and balance the following reactions, which involve heavy-ion bombardments:

(a) 63Li + 5628Ni → ?

(b) 4020Ca + 24896Cm → 14762Sm + ?

(c) 8838Sr + 8436Kr → 11646Pd + ?

(d) 4020Ca + 23892U → 7030Zn + 4 10n + 2 ?

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Textbook 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 24997Bk with accelerated ions of an isotope which we will denote Q. The product atom, which we will call Z, immediately releases neutrons and forms 294117Ts: 24997Bk + Q → Z → 294117Ts + 3 10n (a) What are the identities of isotopes Q and Z? (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 296116Lv. What was the target isotope with which Q collided in this experiment?