Transcript Principal Quantum Number

de Broglie combined Einstien’s E = mc2 and
Planck’s E = hv
 hv = mc2
 Substitute v = c/λ
hc = mc2
λ
 Divide both sides by c: h =mc
λ
Or λ = h
momentum
mc
Wavelength could be predicted by the mass and
speed of the particle.

Challenge Problem 3

The diameter of a US penny is 19mm. The
diameter of a silver atom is only 2.88 Å.
How many silver atoms could be arranged
side by side in a straight line across the
diameter of a penny? (108Å = 1cm)
What do
you
see?
Young
woman
or old
woman?
Review


Light of a particular wavelength (λ) has a
particular frequency (v) and energy.
E = h∙v
and
c = λ∙v
c=3.0 x 108 m/s speed of light
h=6.63 x 10-34 joule-sec Plank’s constant
Why each element produces a
unique line spectra?

Newtonian mechanics- describes objects
at ordinary velocities (classical mechanics)
Quantum mechanics- describes particles at
velocities near that of light (subatomic
particles).

Quantum- a packet of energy

Heisenberg’s Uncertainty Principle

It is impossible to know both the location
and the velocity of an electron at the
same time.
- to “see” an electron we would have to
bounce light off of it which would change
its velocity.
Why did Werner Heisenberg hate
driving cars?
 Because,
every time he looked
at the speedometer he got
lost!
Schrödinger

Treated electrons as a wave
Radial Probability for an electron
The area of highest probability forms the electron cloud
Locating Electrons
Principle quantum number (n)
Sublevel (l)
Orbital (m)
Spin (s)
Principle quantum number (n)
Energy levels are a particular distance
from the nucleus.
2
n=
1
8
2
18
3
32 electrons
4
Principal Quantum Number (n)

The maximum number of electrons at
each energy level is 2n2.
at n = 1, there can be 2(1)2=2 electrons
at n = 2, there can be 2(2)2=8 electrons
at n = 3, there can be 2(3)2=18 electrons
Sublevel (l)


Tells the shape
Each energy level has a number of sublevels
equal to n.
Energy level (n)
1
2
3
4
sublevels
1s
2s,2p
3s,3p,3d
4s,4p,4d,4f
Orbital Orientation (m)

Each orbital can hold up to two electrons.
sublevel
# orbitals
# electrons
s
1
2
p
3
6
d
5
10
f
7
14
“d” orbitals
Spin (s)
indicates the direction of spin on the
electron. ih
Pauli Exclusion Principle states that
no two electrons in an atom can have the
same set of four quantum numbers.
The two electrons in an orbital must have
opposite spins.
Electron configuration notation
He has 2 electrons, so its electron
No. of electrons
2
configuration would be 1s
Li
N
Ne
Na
Principle
quantum
number
1s22s1
1s22s22p3
1s22s22p6
1s22s22p63s1 or [Ne]3s1
sublevel
Degenerate orbitals have the same energy
1s
2s 2p
3s 3p 3d
4s 4p 4d 4f
5s 5p 5d 5f
6s 6p 6d 6f
7s 7p 7d 7f
Sublevels fill in order of increasing energy.
1s2s2p3s3p4s3d4p5s4d5p6s4f5d6p7s5f6d7p
Predicting electron configurations
from the periodic table.
Aufbau Principle- electrons first
occupy the lowest energy level
available.
Electron Dot Notation- show only the
valence electrons, those in the outermost
energy level.
H∙ He: Li∙ Be: Mg:
Orbital notation
1s 2s 2p
N (7)
E
F (9)
E E
E
h h
E
h
E h
Hund’s rule- orbitals of equal energy are
each occupied by one electron before any
orbital is occupied by a second electron, and
all electrons in singly occupied orbitals must
have the same spin.
Principal sublevel Orbitals Orbitals Electrons Electrons
quantum
per
per
per
per energy
number
sublevel energy sublevel level
level
1
s
1
1
2
2
2
s
p
1
3
4
2
6
8
3
s
p
d
1
3
5
s
p
d
f
1
3
5
7
4
9
2
6
10
18
16
2
6
10
14
32


Excited state- electrons in a higher than
normal energy state
N: 1s22s22p3 in ground state
1s22s22p23s1 or
1s22s22p23p1 in excited state
Ions- lost or gained electrons




Anions are negatively charged, having gained
Cations are positively charged, having lost
Na+ 1s22s22p63s1
Cl- 1s22s22p63s23p5 6

Filled and half-filled sublevels are more
stable than partially filled sublevels.
E E EEE E EEE h h h h _
1s 2s
2p
3s 3p
3d

_
4s
Thus Cr takes an electron from 4s to put
one electron in each of its 3d orbitals and
Cu takes a 4s electron to fill each of its 3d
orbitals.