Transcript ElectronsinAtom

From Bohr Atom to Periodic Table
•Bohr Atom: electron energy is quantized, n = 1,2,3,... – are
principal quantum numbers: only some definite electron
orbits are allowed
•Dual nature of electron: particle & wave.
Uncertainty principle: one can’t determine at the same
time both the position & velocity [hence energy] of
electron. Therefore:
•Bohr trajectories transform into ORBITALS, i.e. parts
of space where electron is likely to be found. Their
energies are quantizied
• A set of 4 quantum numbers & gives electron density
distribution around the atomic nucleus
Radial distribution of
electron density
Bohr radius 52.9 pm
2
0
50
100
150 pm
Distance from nucleus
FOUR QUANTUM NUMBERS
Principal quantum #
n = 1, 2, 3, …
distance &energy
Orbital quantum # l = 0, 1,…, n-1
i.e. total n values for each n
shape of orbital
Magnetic orbital quantum #
ml = 0, +1, +2,...,+l
i.e. total (2l +1) values for each l
Spin quantum #
s = + 1/2
Every possible set of quantum #’s
n, l, m gives one orbital
e.g. n=2, l = 1, ml = 0
Pauli Exclusion Principle
there cannot be two electrons in an
atom with all their quantum #'s
equal.
Max number of orb’s
at any nth level is
2
n
Max number of e-'s at any nth
level is 2n2
Energy
level sublevel
(shell) (subshell)
#
of
spin
s=
#
of
orb's 1/2
1
4
e-'s
2
8
n
l
ml
1
2
0
0
1
0
1
2
0
1
3
0
0
0,1
0
9
0,1
0,1,2
0
16
0,1
0,1,2,3
3
4
18
32
LETTER NOTATIONS
l=0
s
1
p
2
d
n=1
1s
3
f
2
with 2
's
l=0
e-
Not every combination make sense!
3
1s
4
2p
2d
3
How many more e's
possible?
SHAPE & NUMBER
of ORBITALS
s
p
spheric, one only!
3 mutually  dumbshells,
px , py, pz
d
5 orb's (l=2, 2l+1=5)
(3)
(1)
d - orbitals
(1)
AUFBAU PRINCIPLE
Orbitals are filled with e-'s according to
their increasing energies, from bottom
to top.
The energy is determined by two
quantum #'s,
n
& l.
The energy increases as (
n + l).
n l
If for 2 orbitals ( + ) is same,
first filled is the orbital with
smaller
n:
Example: Out of two orbitals with the same
n+l =3:
n = 3, l = 0 vs. n = 2, l = 1
2p orbital is filled before 3s
Example: Out of 3 orb's
with the same n+l = 5:
(n=3, l = 2); (n=4, l=1); (n=5, l=0)
3d
4p
5s
st
1 filled is 3d
nd
2 is 4p
rd
3 is 5s
Energy Level Diagram
3d __ __ __ __ __
4s __
3p __ __ __
3s __
2p __ __ __
2s __
1s __
PERIODIC TABLE: s, p, d, f -blocks
p
s
d
f
Hund Rule
When several orb's of equal energy
(“degenerate”) available, e- first fill each of
them one by one, all having the same spins
().
Only after each orbital of the same
subshell got one e-, the 2nd one is placed on
the same orbital. Their spins are
antiparallel (, "el. pair")
:
subshell.
Example there are
3 orb's at p
Electrons fill all of them first one by
one, then each of them may accept the
nd
2 electron.
Example:
How many unpaired e-'s are there
in 3p4 orbital?
ELECTRON PAIRS
Each orbital ma be populated by 1 or 2 electrons.
Pauli Exclusion Principle: there cannot be two electrons in an
orbital, with all their quantum numbers equal. Therefore, if n, l
& ml for 2 electrons are the same,i.e. they belong to the same
orbital, their SPINS MUST BE OPPOSITE (s = + ½). Those
electrons are paired.
The physical reason of pairing electrons is that each electron is
a small magnet. 2 electrons may cancel each other’s magnetic
field  (we say they have antiparallel SPINS, this is a more
stable situation: an electron pair at the same molecular orbital)
or sum up their magnetic field  (unstable situation: both
electrons cannot belong to the same orbital)
repel
S
S
N
N
H2 molecule
N
S
attract
electron pair

He atom
1st period
He 1s2
H 1s
2nd period
Li1s22s Be1s22s2 B1s22s22p1 C1s22s22p2 ... F1s22s22p5 Ne1s22s22p6
…
Hund rule
4th period
K1s22s22p63s23p64s1 Ca[Ar]4s2 Sc[Ar]4s23d1…Zn[Ar]4s23d10 Ga[Ar]4s23d104p1