Quantum Numbers
Fundamentals:
- The letters are n, l, ml, ms
- These correspond with electronic configurations of an element's atom
- 1)Prinicpal Quantum Number (n):
- Capacity to hold a certain number of electrons - 2n^2
- Max # electrons in a given shell – 2n^2
- Difference in energy btwn two shells DEC as the distance from the nucleus INC
- Larger n directly related to the radius and energy
- There are n possible values for azimuthal quantum number since 0 is included as a possible value
- MEANING:
- n=1 therefore 1 possible subshell = s
- n=2 therefore 2 possible subshells = s and p
- n=3 therefore 3 possible subshells = s, p and d
- n=4 therefore 4 possible subshells = s, p, d and f AND SO ON
- 2)Azimuthal Quantum Number(l): shape and number of subshells, chemical bonding and bond angles - (n-1) including 0
- a)s subshell: l=0
- b)p subshell: l=1
- c)d subshell: l=2
- d)f subshell: l=3
- THINK "Sensual People Do Foreplay" - s, p, d, f. Then it follows the alphabet: g, h, i, j, k, etc.
Important EQTN:
Max # electrons per subshell: 4l + 2
Energies of the subshells INC with INC l value
Conceptual Application of EQTN
w/ shell model in mind, each circle/shell=n
w/ ea shell or n includes subshells in that circle/shell
Meaning:
n=1 only 1s = 2electrons max per shell
OR 4(0)+2=2
n=2 2s, 2p = (2+6) [when using the azimuthal numbers]= 8 electrons max per shell
OR s subshell + p subshell; [4(0)+2]+[ 4(1)+2]
n=3 3s, 3p, 3d = (2+6+10) [when using azimuthal numbers] = 18 electrons max per shell
OR s subshell + p subshell + d subshell; [4(0)+2]+[4(1)+2]+[4(2)+2]
n=4 4s, 4p, 4d, 4f = (2+6+10+14) [ when using azimuthal numbers] = 32 electrons max per shell
OR s subshell +p subshell + d subshell + f subshell; [4(0)+2]+[4(1)+2]+[4(2)+2]+[4(3)+2]
- 3)Magnetic Quantum Number (ml): particular orbital within a
subshell: area where an electron is highly likely to be found , **btwn
-l and +l including 0
- Important EQTN: Possible Orbitals per subshell: 2l+1 = ml
- 4)Spin Quantum Number (ms): spin orientations, either .5 or-.5, either positive or negative
- Parallel spins: different orbital but same ms
Additional Information:
