Final answer:
Each atomic subshell type has a distinct number of orbitals: there is 1 s orbital, 3 p orbitals, 5 d orbitals, and 7 f orbitals. These are determined by quantum numbers, defining where electrons can be located in an atom.
Step-by-step explanation:
In atomic physics, orbitals within an atom are designated by three quantum numbers: principal (n), azimuthal (l), and magnetic (ml). These correspond to the energy level, shape, and orientation of the orbital, respectively. The number of orbitals within each subshell type (s, p, d, f) is determined by the azimuthal quantum number (l).
- s orbitals – Orbitals with l = 0 are called s orbitals and there is only 1 s orbital for any principal quantum number (n).
- p orbitals – With l = 1, p orbitals are formed, constituting a set of 3 p orbitals due to three possible values of ml (-1, 0, +1).
- d orbitals – For d orbitals where l = 2, there are 5 d orbitals, corresponding to the five values of ml ranging from -2 to +2.
- f orbitals – When l = 3, f orbitals are defined, yielding 7 f orbitals, one for each value of ml from -3 to +3.
Therefore, for each type of subshell, s has 1 orbital, p has 3 orbitals, d has 5 orbitals, and f has 7 orbitals. These orbitals in the subshells are where electrons reside in an atom, with each orbital capable of holding two electrons.