Question

Write isotopic symbols in the form \(\frac{A}{Z}\) for each isotope. \begin{equation} \begin{array}{l}{\text { a. the copper isotope with } 34 \text { neutrons }} \\\ {\text { b. the copper isotope with } 36 \text { neutrons }} \\ {\text { c. the potassium isotope with } 21 \text { neutrons }} \\ {\text { d. the argon isotope with } 22 \text { neutrons }}\end{array} \end{equation}

Short answer

\(\frac{63}{29}\)Cu, \(\frac{65}{29}\)Cu, \(\frac{40}{19}\)K, and \(\frac{40}{18}\)Ar

Step-by-step solution

- Determine the Element's Atomic Number

Locate the element on the periodic table to find its atomic number, which is the number of protons. For copper (Cu), the atomic number is 29. For potassium (K), it is 19. And for argon (Ar), it is 18.

- Determine the Mass Number

The mass number (A) of an isotope is the sum of its protons and neutrons. For the given isotopes, add the number of neutrons to the atomic number of the element to calculate the mass number. For example, for copper with 34 neutrons, A = 29 (protons) + 34 (neutrons) = 63.

- Write the Isotopic Symbols

Isotopic symbols are represented as \(\frac{A}{Z}\) where A is the mass number and Z is the atomic number. Replace A and Z with the appropriate numbers for each isotope.

- Answer for Copper with 34 Neutrons

For copper with 34 neutrons: \(\frac{63}{29}\)Cu

- Answer for Copper with 36 Neutrons

For copper with 36 neutrons: \(\frac{65}{29}\)Cu

- Answer for Potassium with 21 Neutrons

For potassium with 21 neutrons: \(\frac{40}{19}\)K

- Answer for Argon with 22 Neutrons

For argon with 22 neutrons: \(\frac{40}{18}\)Ar

Key concepts

Atomic Number

The atomic number is a fundamental characteristic of an element. It reflects the number of protons found in the nucleus of each atom of that element. The atomic number also defines the element's position on the periodic table and is designated by the symbol 'Z'.

For example, every atom of copper (Cu) has 29 protons, so the atomic number for copper is 29. It is vital to remember that in a neutral atom, the number of protons is equal to the number of electrons. This balance gives the atom its neutral charge. The atomic number is key when identifying isotopes because it remains constant for all isotopes of a given element, whereas the number of neutrons can vary.

Mass Number

The mass number, represented by 'A', is the total number of protons and neutrons in the nucleus of an atom. Unlike the atomic number, the mass number is not found directly on the periodic table and must be calculated for each isotope. To find the mass number, simply add the number of protons (Z) to the number of neutrons (N).

For instance, if we have an isotope of copper with 34 neutrons, we add these neutrons to the 29 protons (from its atomic number) to get a mass number of 63. This calculation is essential for writing isotopic symbols, which showcase both the mass number and atomic number, giving insight into the specific isotope of an element.

Isotopes of Elements

Isotopes are different forms of the same element, which have the same number of protons but a different number of neutrons within their nuclei. This variance in the number of neutrons results in different mass numbers. Isotopes are particularly important because they can exhibit different physical, and sometimes chemical, properties.

Take copper as an example; it can have isotopes with 34 or 36 neutrons. Although both isotopes are still copper, they have different mass numbers. This diversity among isotopes has profound implications, including use in medical imaging, dating archaeological artifacts, and as tracers in biochemical research.

Periodic Table

The periodic table is an organized chart of elements arranged in order of increasing atomic number. Each element is represented by its unique chemical symbol, and elements are situated in specific groups and periods that classify them according to shared properties.

Understanding the arrangement of the periodic table is crucial when studying isotopic symbols, as it allows one to find the atomic number quickly. The table also helps in predicting the chemical behavior of different isotopes and their placement within the context of the elements. Whether you are a student, a researcher, or just curious, the periodic table serves as a valuable tool for navigating the complex world of chemistry and understanding the subtle nuances of isotopic differences.