Which quantum number defines the shape of an orbital?

The shape of an orbital is defined by the orbital quantum number, often referred to as 'l'. This quantum number can take on integer values starting from 0 up to n-1, where n is the principal quantum number that indicates the energy level of the electron. Each value of 'l' corresponds to a specific type of orbital: for example, when l = 0, it represents an s orbital (spherical shape), l = 1 corresponds to a p orbital (dumbbell shape), l = 2 refers to a d orbital (more complex shapes), and l = 3 denotes an f orbital (even more complex shapes).

The principal quantum number indicates the size and energy of the orbital but does not determine its shape. The magnetic quantum number (Ml) describes the orientation of the orbital in space but does not affect its intrinsic shape. The spin quantum number (Ms) relates to the spin of the electron and does not influence the spatial characteristics of the orbital.

Thus, it is the orbital quantum number that is essential for defining the specific shape of the orbital in which electrons reside.