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
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