Page 245 - Instant notes

G5
THE STRUCTURE OF THE HYDROGEN
ATOM

Key Notes
The emission spectrum of a hydrogen atom consists of discrete
frequencies, v, of light forming the Rydberg series of groups of
2
2
regular pattern obeying the relationship, v=R H (1/n 1 –1/n 2 ) with
integer values of n 1 and n 2 .
The solution to the Schrödinger equation for a single electron
moving in the attractive Coulombic potential of a positively
charged nucleus produces quantized energy levels whose energy
values are inversely proportional to the square of an integer
quantum number, n. The energy difference between pairs of these
energy levels exactly accounts for the Rydberg series of the
hydrogen atom emission spectrum.
The wavefunction solutions for an electron in an atom are called
atomic orbitals. The boundary conditions impose three quantum
numbers on the orbitals: principal quantum number, n(1, 2,…);
orbital angular momentum quantum number, l(0, 1…n−1);
magnetic quantum number, m l (−l, .. 0,…l). All orbitals with the
same value of n constitute a shell. Orbitals with different values
of l constitute sub-shells of the shell. Orbitals with l=0, 1, 2, 3 are
called s, p, d, f, orbitals respectively. All orbitals in a sub-shell of
a hydrogenic atom are degenerate.
All s orbitals are spherically symmetric about the center of the
atom whereas the shapes of p and d orbitals vary with angular
direction. The three p orbitals have lobes pointing along the x, y,
and z axes, respectively. The five d orbitals have more complex
angular shapes. The radius of maximum probability of electron
location in a shell of s, p, or d orbitals increases with principal
quantum number.
Related topics Quantization of energy and Valence bond theory (H2)
particle-wave duality (G3)
Molecular orbital theory of
diatomic molecule I (H3)
The wave nature of matter (G4)
Many-electron atoms (G6)