The third quantum number is the magnetic quantum number and is designated ml. An orbital is a
specific region within a subshell that may contain no more than two electrons. The magnetic
quantum number specifies the particular orbital within a subshell where an electron is highly likely
to be found at a given point in time. The possible values of ml are all integers from l to –l, including
- Therefore, the s subshell, where there is one possible value of ml (0), will contain 1 orbital;
likewise, the p subshell will contain 3 orbitals, the d subshell will contain 5 orbitals, and the f
subshell will contain 7 orbitals. The shape and energy of each orbital are dependent upon the
subshell in which the orbital is found. For example, s orbitals (l = 0, ml = 0) are all spherical in shape.
Those with larger principal quantum numbers have a larger radius, implying a larger average
distance from the nucleus. A p subshell has three possible ml values (–1, 0, +1). The three dumbbell-
shaped orbitals are oriented in space around the nucleus along the x, y, and z axes, and are often
referred to as px, py, and pz.
The magnetic quantum number can also play a part in determining the shape of an orbital: Orbitals
in the d and f subshells, for example, may have different shapes (in addition to just different
orientations) depending on the value of ml.
Spin Quantum Number
BASIC CONCEPT
The spin quantum number is either or , regardless of values of other quantum
numbers.The fourth quantum number is also called the spin quantum number and is denoted by ms.
Regardless of the shell, subshell, or orbital, any electron can have only one of two values for the spin
quantum number.