Question

Indicate the number of protons and neutrons in the following nuclei: (a) \({ }_{52}^{124} \mathrm{Te},(\mathbf{b}){ }^{37} \mathrm{Cl},(\mathrm{c})\) thorium- \(232 .\)

Short answer

(a) \({}_{52}^{124} \mathrm{Te}\): 52 protons and 72 neutrons (b) \({}^{37} \mathrm{Cl}\): 17 protons and 20 neutrons (c) Thorium-232: 90 protons and 142 neutrons

Step-by-step solution

Identify the atomic number and mass number for each element

In order to determine the number of protons and neutrons in a nucleus, we first have to identify the atomic number and mass number for each element. The atomic number (Z) represents the number of protons in an element, and the atomic mass number (A) represents the total number of protons and neutrons inside the nucleus. For the exercise, we have three nuclei: (a) \({}_{52}^{124} \mathrm{Te}\): The atomic number (Z) is 52 and the mass number (A) is 124. (b) \({}^{37} \mathrm{Cl}\): The atomic number is not given, but we know it's Chlorine, which has an atomic number (Z) of 17. The mass number (A) is 37. (c) Thorium-232: The atomic number (Z) for Thorium (Th) is 90 and the mass number (A) is 232.

Calculate the number of protons

The number of protons is equal to the atomic number (Z) for each element. So, for each case: (a) \({}_{52}^{124} \mathrm{Te}\): The number of protons is 52. (b) \({}^{37} \mathrm{Cl}\): The number of protons is 17 (as Chlorine has an atomic number of 17). (c) Thorium-232: The number of protons is 90.

Calculate the number of neutrons

The number of neutrons can be found by subtracting the atomic number (Z) from the atomic mass number (A). Neutrons = A - Z For each case: (a) \({}_{52}^{124} \mathrm{Te}\): The number of neutrons is 124 - 52 = 72. (b) \({}^{37} \mathrm{Cl}\): The number of neutrons is 37 - 17 = 20. (c) Thorium-232: The number of neutrons is 232 - 90 = 142.

Final Answer

Summarizing our results for each nucleus: (a) \({}_{52}^{124} \mathrm{Te}\): 52 protons and 72 neutrons (b) \({}^{37} \mathrm{Cl}\): 17 protons and 20 neutrons (c) Thorium-232: 90 protons and 142 neutrons

Key concepts

Atomic Number

The atomic number, symbolized as 'Z', is fundamental to understanding elements and their identities. It denotes the number of protons in the nucleus of an atom, which is unique for each element. For example, in the exercise, chlorine is identified by its atomic number as 17, signifying it contains 17 protons. This is more than just a count; the atomic number determines the chemical properties of the element and its place in the periodic table.

In essence, when you know the atomic number of an element, you can predict how it will interact with other elements. For students, remembering that 'Z equals protons' can be a simple way to keep track of an element's identity.

Mass Number

The mass number, denoted as 'A', represents the total count of protons and neutrons in an atom's nucleus. It is the sum that gives us an understanding of the atom's mass. When you see an element symbol like \( {}_{52}^{124} \mathrm{Te} \), the upper number, 124, is its mass number. To find the number of neutrons, which lack a dedicated spot on the element symbol, you subtract the atomic number from the mass number, such as \( 124 - 52 = 72 \) neutrons in Tellurium-124.Being able to calculate the number of neutrons is essential, as it helps us understand isotopes—variations of the same element with different numbers of neutrons—and their distinct properties. The mass number gives us a quick snapshot of the nucleus's composition.

Protons and Neutrons

Protons and neutrons are known as nucleons and form the atomic nucleus. They are nearly equal in mass, but only protons are charged, whereas neutrons are neutral. This balance of charge and mass plays a crucial role in the stability of an atom. As seen in the homework solutions, the number of protons remains constant within an element but neutrons can vary, leading to various isotopic forms. For instance, Thorium-232, as explained in the solution, has 90 protons and 142 neutrons. The different interactions between these nucleons are what make nuclear physics so fascinating. In teaching students about protons and neutrons, highlight the link between the number of neutrons and the isotopic nature of an atom, as well as the role that the electrically charged protons play in chemical reactions.