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.

Verified step by step guidance

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.
2. 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).
3. 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.
4. 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.
5. 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.

Key Concepts

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.

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.

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.