Skill 17.4 Demonstrating a basic understanding of quantum numbers

Skill 17.4 Demonstrating a basic understanding of quantum numbers 

The quantum-mechanical solutions from the Schrodinger Equation utilize three quantum numbers n, I, and mj) to describe an orbital and a fourth (n s) to describe an electron in an orbital. This model is useful for understanding the frequencies of radiation emitted and absorbed by atoms and chemical properties of atoms. 

The principal quantum number n may have positive integer values (1. 2. 3,. ..). n is a measure of the distance of an orbital from the nucleus, and orbitals with the same value of n are said to be in the same shell. This is analogous to the Bohr model of the atom. Each shell may contain up to 2n electrons. The highest quantum number n that any shell of an element has is the same as the number of the row of the periodic table in which the element is found. 

The azimuthal quantum number / may have integer values from 0 to n-1. / describes the angular momentum of an orbital. This determines the orbital s shape. Orbitals with the same value of n and / are in the same subshell, and each subshell may contain up to 4/ + 2 electrons. Subshells are usually referred to by the principle quantum number followed by a letter corresponding to I as shown in the following table  

Therefore, s subshells may have 4 x 0 + 2 = 2 electrons, and p subshells may have 4x1 +2 = 6 electrons. Helium is in the first row of the periodic table, and has only a single s subshell with two electrons. This subshell would be notated as Is. 

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