Download Quantum Numbers

Arrangement of Electrons in
Atoms
• Principles of electromagnetic radiation led
to Bohr’s model of the atom.
• Electron location is described using
identification numbers called quantum
numbers.
• Rules for expressing electron location
results in a unique electron configuration
for each element.
Mullis
1
Wave Description of Light
• Electromagnetic radiation is a form of energy that
exhibits wavelike behavior as it travels through space
• Wavelength (λ)
– Distance between corresponding points on adjacent waves.
– Unit: nm,cm,m
• Frequency (ν)
– Number of waves that pass a specific point in a given time
– Unit: Hz or waves/sec
Recall that Speed = Distance/time (m/sec)
• Speed of light (c)
C=λν
Mullis
2
Behavior of Light
• Photoelectric effect
– The emission of electrons when light shines on
the metal
– Scientists found that below a certain frequency,
no electrons were emitted.
– Light also behaves as a particle: Since hot
objects do not emit em energy continuously,
they must emit energy in small chunks called
quanta.
• Quantum
– Minimum quantity of energy that can be gained
or lost by an atom
Mullis
3
Light as a particle and a wave
Planck and Einstein
• Max Planck: Relationship between quantum of
energy and wave frequency
• Planck’s constant h = 6.626 x 10-34 J-s
E = hν
E is energy, ν is frequency
• Albert Einstein: Established dual wave-particle
nature of light 1st
– Einstein explained PE effect by proposing that EM
radiation is absorbed by matter only in whole numbers
of photons.
– Electron is knocked off metal surface only if struck by
one photon with certain minimum energy.
Mullis
4
Louis de Broglie
• Because we know that light has a particle nature, we might ask if matter has
wave nature.
• Louis de Broglie answered this. His equation:
λ = h/mv
• Lambda is a wave property.
• Momentum (mass x velocity) is a particle property.
• In one equation, de Broglie summarized the concepts of
waves and particles as they apply to high-speed, low mass
objects.
• Results of de Broglie’s discovery include X-ray diffraction
and electron microscopy techniques used to study small
objects.
Mullis
5
Quantum Theory
• Ground state: An atom’s lowest energy state
• Excited state: Higher potential energy than ground
state.
• Photon: A particle of electromagnetic radiation
having zero mass and carrying a quantum of energy
(i.e., packet of light)
• Only certain wavelengths of light are emitted by
hydrogen atoms when electric current is passed
through—Why?
Mullis
6
Niels Bohr links hydrogen’s
electron with photon emission
• Bohr proposed that an electron circles the
nucleus in allowed orbits at specific energy
levels.
– Lowest energy is close to nucleus
• Bohr’s theory explained the spectral lines
seen in hydrogen’s line emission spectrum,
but it did not hold true for other elements.
Mullis
7
Quantum Numbers
•
•
•
•
Principal quantum number, n
Angular momentum quantum number, l
Magnetic quantum number, ml
Spin quantum number, ms
Mullis
8
Azimuthal quantum number =
Angular momentum quantum number
• Depends on the value of n
• Values of l starts at 0 and increases to n-1
• This number defines the shape of the
orbital.
Orbital
s
p
d
f
Mullis
l
0
1
2
3
9
Magnetic quantum number
• Magnetic quantum number is the orientation of an
orbital around the nucleus.
• It is the number of orbitals in a sublevel.
Orbitals per sublevel
The s sublevel has 1 orbital.
The p sublevel has 3 orbitals.
The d sublevel has 5 orbitals.
The f sublevel has 7 orbitals.
Mullis
s
p
d
f
1
3
5
7
10
Quantum numbers
1s ____
2s ____
2p ____ ____ ____
3s _____
Principal quantum number
Magnetic quantum number
Angular momentum quantum number
Mullis
11
Quantum numbers
1s ____
2s ____
ms = -1/2
2p ____ ____ ____
ml = -1
3s _____
ml =0
ms = +1/2
ml = +1
Magnetic quantum number
Principal quantum number
Angular momentum quantum number
[ for a p orbital, l = 1]
Mullis
12
Magnetic quantum number, ml
• Gives the 3d orientation of each orbital.
• Has value from –l to + l
• Example:
3p refers to orbitals with n = 3 and l = 1.
Values of ml = -1,0,1
• These three numbers correspond the 3 possible
orientations of the dumbbell-shaped p orbitals
(x,y and z axis).
Mullis
13