7.10
Quantum Numbers
View the full transcript and gain access to JoVE Core videos
Q1: What does the principal quantum number tell you about an electron?
The principal quantum number, n, denotes the energy level to which an electron belongs and can have integer values of 1, 2, 3, and so forth. The greater the value of n, the farther the electron is from the nucleus. It defines the general size and energy of the orbital, essentially describing the shell number in which an electron resides.
Q2: How does the angular momentum quantum number relate to orbital shape?
The angular momentum quantum number, l, describes the shape of the orbital that the electron occupies. It can have integer values from 0 to n – 1 for each value of n. Orbitals with l = 0 are s orbitals, l = 1 are p orbitals, l = 2 are d orbitals, and l = 3 are f orbitals, each with distinct shapes.
Q3: What does the magnetic quantum number describe about an electron's orbital?
The magnetic quantum number, ml, describes the orientation in space of the orbital that the electron occupies. It can have any integer value between –l and +l, including zero. The number of possible orientations for a given subshell equals 2l + 1, so a p subshell with l = 1 has three possible orientations.
Q4: Why was a fourth quantum number needed to explain atomic spectra?
When hydrogen-line spectra were examined at extremely high resolution, some lines appeared as pairs of closely spaced lines rather than single peaks, revealing fine structure. This indicated additional small energy differences for electrons in the same orbital, leading scientists to propose the spin quantum number to account for these observations.
Q5: What are the two possible values for electron spin?
Electrons are spinning charges that behave like tiny bar magnets. The two possible spinning motions are clockwise, indicated by a spin quantum number ms of +1/2, and counterclockwise, indicated by ms of –1/2. These are the only two spin states available to an electron in an orbital.
Q6: How many orbitals exist in different subshells?
The number of orbitals in a subshell is determined by the formula 2l + 1. An s subshell (l = 0) contains one orbital, a p subshell (l = 1) contains three orbitals, a d subshell (l = 2) contains five orbitals, and an f subshell (l = 3) contains seven orbitals.
Q7: How are the first three quantum numbers related to each other?
The principal quantum number n determines the possible values of the angular momentum quantum number l, which ranges from 0 to n – 1. The magnetic quantum number ml then depends on l, ranging from –l to +l. Together, these three interrelated quantum numbers define where in space an electron is most likely to be located.