Example:
What is the energy release when the hydrogen electron goes from n = 5 to n = 2?
E = 2.18 * 10^{–18} J = 2.18 * 10^{–18} J
= – 4.58 * 10^{–19} J
What is the wavelength of the light needed to remove the hydrogen electron from its ground state?
 n_{i} = 1 and n_{f} = ∞ (completely removed from the atom)
 Calculate E:
E = 2.18 * 10^{–18} J = 2.18 * 10^{–18} J
= 2.18 * 10^{–18} J
Note:
 Calculate the wavelength:
9.11 * 10^{–8} m = 91.1 nm
Quantum Numbers
Four quantum numbers describe the position and behavior of an electron in an atom: the principal quantum number, the angular momentum quantum number, the magnetic quantum number, and the electron spin quantum number. A branch of physics called quantum mechanics mathematically derives these numbers through the Schrödinger equation.
Principal quantum number ( n) The principle quantum number is the energy level of the electron given the designation n. The value of n can be any integer (1, 2, 3, 4 . . .) and determines the energy of the orbitals.
Angular momentum quantum number ( l) The angular momentum is the subshell designation of an electron and describes the shape of the orbital. These subshells are described by the letter l. The possible l values for a particular energy level are 0 to (n – 1). The l values are also given a letter designation. The l value is 0, 1, 2, 3, or 4, and the designation is s, p, d, f, or g.
Magnetic quantum number (m_{l}) The magnetic quantum number (m_{l}) describes the orbital's orientation in space. For a given l value, ml has integer values from –l to +l. In other words, for the p subshell (l = 1), the m_{l} values are –1, 0, and +1, hence three orbitals.
Electron spin quantum number (m_{s}) The electron spin quantum number describes the spin of an electron. Magnetic fields have shown that the two electrons in an orbital have equal and opposite spins. The m_{s} values for these spins are and .
Example:
Are the following possible sets of quantum numbers? Explain.
(1, 1, 1, ); (2, 1, 0, ); (3, 2, 1, 1)
(1, 1, 1,): Not possible. For n = 1, l can only be 0, not 1.
(2, 1, 0, ): Possible.
(3, 2, 1, 1): Not possible. m_{s} can only be or .
Practice problems for these concepts can be found at  Atomic Structure Practice Questions
 1

2
Ask a Question
Have questions about this article or topic? AskRelated Questions
See More QuestionsPopular Articles
 Kindergarten Sight Words List
 First Grade Sight Words List
 10 Fun Activities for Children with Autism
 Signs Your Child Might Have Asperger's Syndrome
 Theories of Learning
 A Teacher's Guide to Differentiating Instruction
 Social Cognitive Theory
 Child Development Theories
 Curriculum Definition
 Why is Play Important? Social and Emotional Development, Physical Development, Creative Development