<P> Generally speaking, the number n determines the size and energy of the orbital for a given nucleus: as n increases, the size of the orbital increases . When comparing different elements, the higher nuclear charge Z of heavier elements causes their orbitals to contract by comparison to lighter ones, so that the overall size of the whole atom remains very roughly constant, even as the number of electrons in heavier elements (higher Z) increases . </P> <P> Also in general terms, l determines an orbital's shape, and m its orientation . However, since some orbitals are described by equations in complex numbers, the shape sometimes depends on m also . Together, the whole set of orbitals for a given l and n fill space as symmetrically as possible, though with increasingly complex sets of lobes and nodes . </P> <P> The single s - orbitals (l = 0 (\ displaystyle \ ell = 0)) are shaped like spheres . For n = 1 it is roughly a solid ball (it is most dense at the center and fades exponentially outwardly), but for n = 2 or more, each single s - orbital is composed of spherically symmetric surfaces which are nested shells (i.e., the "wave - structure" is radial, following a sinusoidal radial component as well). See illustration of a cross-section of these nested shells, at right . The s - orbitals for all n numbers are the only orbitals with an anti-node (a region of high wave function density) at the center of the nucleus . All other orbitals (p, d, f, etc .) have angular momentum, and thus avoid the nucleus (having a wave node at the nucleus). Recently, there has been an effort to experimentally image the 1s and 2p orbitials in a SrTiO crystal using scanning transmission electron microscopy with energy dispersive x-ray spectroscopy . Because the imaging was conducted using an electron beam, Coulombic beam - orbital interaction that is often termed as the impact parameter effect is included in the final outcome (see the figure at right). </P> <P> The shapes of p, d and f - orbitals are described verbally here and shown graphically in the Orbitals table below . The three p - orbitals for n = 2 have the form of two ellipsoids with a point of tangency at the nucleus (the two - lobed shape is sometimes referred to as a "dumbbell"--there are two lobes pointing in opposite directions from each other). The three p - orbitals in each shell are oriented at right angles to each other, as determined by their respective linear combination of values of m . The overall result is a lobe pointing along each direction of the primary axes . </P>

Who discovered that an electron's energy depends on its distance from the nucleus