Transcript Bohr and Quantum Mechanical Model

Bohr and Quantum
Mechanical Model
Mrs. Kay
Chem 11A
Those who are not shocked
when they first come across
quantum theory cannot possibly
have understood it.
(Niels Bohr on Quantum Physics)
Wavelengths and energy
Understand that different wavelengths
of electromagnetic radiation have
different energies.
 c=vλ

c=velocity of wave
 v=(nu) frequency of wave
 λ=(lambda) wavelength

Bohr also postulated that an atom
would not emit radiation while it was in
one of its stable states but rather only
when it made a transition between
states.
 The frequency of the radiation emitted
would be equal to the difference in
energy between those states divided
by Planck's constant.

E2-E1= hv
h=6.626 x 10-34 Js = Plank’s constant
E= energy of the emitted light (photon)
v = frequency of the photon of light




This results in a unique emission spectra for each
element, like a fingerprint.
electron could "jump" from one allowed energy state
to another by absorbing/emitting photons of radiant
energy of certain specific frequencies.
Energy must then be absorbed in order to "jump" to
another energy state, and similarly, energy must be
emitted to "jump" to a lower state.
The frequency, v, of this radiant energy corresponds
exactly to the energy difference between the two
states.
In the Bohr model, the electron is in a
defined orbit
 Schrödinger model uses probability
distributions for a given energy level
of the electron.

Orbitals and quantum
numbers
Solving Schrödinger's equation leads
to wave functions called orbitals
 They have a characteristic energy and
shape (distribution).


The lowest energy orbital of the hydrogen
atom has an energy of -2.18 x 1018 J and
the shape in the above figure. Note that in
the Bohr model we had the same energy
for the electron in the ground state, but that
it was described as being in a defined orbit.

The Bohr model used a single
quantum number (n) to describe an
orbit, the Schrödinger model uses
three quantum numbers: n, l and ml
to describe an orbital
The principle quantum
number 'n'
Has integral values of 1, 2, 3, etc.
 As n increases the electron density is
further away from the nucleus
 As n increases the electron has a
higher energy and is less tightly
bound to the nucleus

The azimuthal or orbital
(second) quantum number 'l'
Has integral values from 0 to (n-1) for
each value of n
 Instead of being listed as a numerical
value, typically 'l' is referred to by a
letter ('s'=0, 'p'=1, 'd'=2, 'f'=3)
 Defines the shape of the orbital

The magnetic (third) quantum
number 'ml'
Has integral values between 'l' and -'l',
including 0
 Describes the orientation of the orbital
in space

For example, the electron orbitals
with a principle quantum number of 3
n
l
Subshell
ml
Number of
orbitals in
subshell
3
0
3s
0
1
1
3p
-1,0,+1
3
2
3d
-2,1,0,+1,+2 5


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the third electron shell (i.e. 'n'=3) consists of
the 3s, 3p and 3d subshells (each with a
different shape)
The 3s subshell contains 1 orbital, the 3p
subshell contains 3 orbitals and the 3d
subshell contains 5 orbitals. (within each
subshell, the different orbitals have different
orientations in space)
Thus, the third electron shell is comprised of
nine distinctly different orbitals, although
each orbital has the same energy (that
associated with the third electron shell) Note:
remember, this is for hydrogen only.
Subshell
Number of orbitals
s
1
p
3
d
5
f
7
Practice:
What are the possible values of l and ml
for an electron with the principle
quantum number n=4?
 If l=0, ml=0
 If l=1, ml= -1, 0, +1
 If l=2, ml= -2,-1,0,+1, +2
 If l=3, ml= -3, -2, -1, 0, +1, +2, +3

Problem #2
Can an electron have the quantum
numbers n=2, l=2 and ml=2?
 No, because l cannot be greater than
n-1, so l may only be 0 or 1.
 ml cannot be 2 either because it can
never be greater than l


In order to explain the line spectrum of hydrogen, Bohr made one
more addition to his model. He assumed that the electron could
"jump" from one allowed energy state to another by
absorbing/emitting photons of radiant energy of certain specific
frequencies. Energy must then be absorbed in order to "jump" to
another energy state, and similarly, energy must be emitted to
"jump" to a lower state. The frequency, v, of this radiant energy
corresponds exactly to the energy difference between the two
states. Therefore, if an electron "jumps" from an initial state with
energy Ei to a final state of energy Ef, then the following equality
will hold:
(delta) E = Ef - E i = hv
To sum it up, what Bohr's model of the hydrogen atom states is that
only the specific frequencies of light that satisfy the above equation
can be absorbed or emitted by the atom.