Quantum Numbers and orbitals

slide 1 for chem 3

principle quantum number

n

angular momentum quantum number

l

magnetic quantum number

ml

electron spin quantum number

ms

Principal Quantum Number (n)

the energy and the probable distance of the electron from the nucleus, the larger the n=the further the electron is from the nucleus, describes the shell where the electron is located, can have a positive, non-zero, whole number value

Angular Momentum Quantum number (l)

the shape of the orbital where the electron is located, describes in which subshell the electron is located, can have a non-negative whole number value including zero (cannot be greater than n-1)

Magnetic Quantum Number (ml)

The orientation of the orbital where the electron is located (what direction the orbital is pointing in or how it’s angled) ,can have a negative positive or zero whole number value (from -l to +l)

Spin Quantum number (ms)

The orientation of the electron “spin”, can only have two values= -1/2 (spin down) and +1/2 (spin up)

subshells

The number of subshells in a principal electron shell is equal to the number of possible l values, l=0→s, l=1→p, l=2→d, l=3→f, to designate/ name a certain subshell use n value and letter value for l, ex 4d

s orbital

l=o→s orbital, look like spheres

the p orbitals

l=1→ p orbital, have two lobes of electron density on both sides of nucleus (looks like a dumbbell), node is located on the nucleus as a plane

d orbital

l=2→ d orbitalm have multiple nodes and multiple lobes, 4 look like clovers with angular nodes between lobes and one looks like a dumbbell with a ring with angualar nodes around vertical lobes

electron probability

probability of finding the electron within a certain space, bc of heisenberg uncertainty principle the electron is “smeared” everywhere at once ununiformly, orbitals do not have sharp boundaries the probability of finding the electron at a large distance from the nucleus is tiny but never zero

nodes

an area where the elctron density is 0, as n increases the number of nodes increases (total # of nodes=n-1)

types of nodes

radial-spherical (# of radial nodes=n-l-1) angular nodes-planes (# of angular nodes=l)

energy diagrams in a single-electron atom

All subshells with the same n are degenerate or are equal in energy, the only forces acting on the electron are kinetic energy and the electrostatic attraction between the negative electron and the positive nucleus (so we can use the bohr model)

energy diagrams in multi-electron atom

sublevels within the same principal energy level are no longer degenerate, electrons interact with each other changing the energy levels

electron sheilding

electrons closer to the nucleus “sheild” further electrons from the nuclear attraction, this causes a lower effective nuclear charge on those further electrons and because of less attraction from the nucleus there is higher energy

electron penetration

Electrons closer to the nucleus can have a greater attraction to the nucleus, bc of the greater attraction, the energy of these electrons is lower (most easily seen with the s orbital, which has no nodes at the nucleus)

orbital energies

the closer to the nucleus, the lower the energy