Atomic Number
The atomic number is a fundamental property of an element and it holds considerable significance in chemistry and physics. Structurally, it defines the number of protons found in the nucleus of an atom, and chemically, it determines the position of the element on the periodic table.
For instance, with the atomic number of 24, we know that the element is chromium (Cr) because each element has a unique atomic number. For a neutral atom, the atomic number also specifies the number of electrons surrounding the nucleus, assuming there are no net charges. In case the atom is an ion, the atomic number still represents the number of protons, but the number of electrons will differ depending on the ion’s charge. A positive charge, as in the exercise, indicates fewer electrons compared to the number of protons.
Quantum Number
A quantum number acts as a quantifier in quantum mechanics, delineating the values of conserved quantities in the dynamics of a quantum system. When discussing electron configurations, we refer to sets of four quantum numbers: the principal, azimuthal, magnetic, and spin quantum numbers.
The principal quantum number, denoted as n, is of particular importance as it specifies the electron shell or energy level of an electron within an atom and impacts the atom's energy and size. For example, as described in the exercise, knowing the electrons’ principal quantum numbers allows us to derive not only the energy levels they occupy (such as n=1 for closest to the nucleus, n=2 for the next, and so forth) but also to predict and understand an ion or atom's electron configuration.
Periodic Table
The periodic table is a tabular arrangement of the chemical elements, ordered by atomic number, electron configuration, and recurring chemical properties. Elements are presented in order of increasing atomic number, and the rows and columns are so arranged to highlight periodic trends among the elements.
Looking at the periodic table, you can locate each element based on its atomic number. This organization aids in predicting the characteristics of elements, and how they might react chemically. From our exercise, knowing the element with atomic number 24 is chromium (Cr) allows us to predict its typical bonding, electron configuration, and reactivity based on its placement in group 6 and period 4 of the table.
Principal Quantum Number
The principal quantum number, denoted by the symbol n, defines the energy level of an electron in an atom. As n increases, the electron's energy and its probable distance from the nucleus also increase. The number corresponds to the row number of the periodic table.
In the given exercise, electrons with principal quantum numbers n=1, n=2, and n=3 are located at different energy levels. These levels can hold a limited number of electrons, typically up to 2n2. For example, the first energy level (n=1) can hold up to 2 electrons, the second up to 8, and the third up to 18. Using these occupancies helps you piece together the electron configuration for the neutral atom.
Neutrons in Nucleus
Neutrons are subatomic particles found in the atomic nucleus. Unlike protons, they carry no charge and contribute significantly to the atom's mass. The number of neutrons in an atom can vary, leading to isotopes, which are atoms of the same element (same number of protons) but with different numbers of neutrons.
In the problem we're analyzing, by subtracting the atomic number from the atom’s mass number (approximated as the atomic mass unit rounded to the nearest whole number), you can calculate the number of neutrons. The mass number represents the total number of protons and neutrons within the nucleus. Detouring around the fact that real atomic masses are affected by binding energy differences and not exactly whole numbers offers a simplified approach suitable for education, allowing students to practice the concept.
