Download Line Spectra and the Bohr Model

Atomic Structure
Wave/Particle Concept
Atomic H Spectrum
Quantization
Bohr Model
Quantum Mechanics
Heisenberg Uncertainty
Quantum Numbers
Applications
Electron Configuration
Electron Affinity
Ionization Energy
Electronegativity
Size
Energy Levels
The Wave Nature of Light
• All waves have a characteristic wavelength, l, and
amplitude, A.
• Frequency, n, of a wave is the number of cycles which
pass a point in one second.
• Speed of a wave, c, is given by its frequency multiplied
by its wavelength:
c  l n
• For light, speed = c = 3.00x108 m s-1 .
• The speed of light is constant!
The Wave Nature of Light
The Wave Nature of Light
The Wave Nature of Light
Wavelength: λ (m)
Frequency: ν (s-1)
Energy: E (J)
X – rays
Microwaves
1.00x10-10 m
1.00x10-2 m
Comment(s)
Quantized Energy and Photons
• Planck: energy can only be absorbed or released from
atoms in certain amounts called quanta.
• The relationship between energy and frequency is
E  h n
where h is Planck’s constant ( 6.626  10-34 J s ) .
Quantized Energy and Photons
The Photoelectric Effect and Photons
• Einstein assumed that light traveled in energy packets
called photons.
• The energy of one photon is:
E  h n
Nature of Waves: Quantized Energy and Photons
Wavelength: λ (m)
Frequency: ν (s-1)
Energy: E (J)
X – rays
Microwaves
1.00x10-10 m
1.00x10-2 m
Comment(s)
Line Spectra and the Bohr Model
•
•
•
•
Line Spectra
Radiation composed of only one wavelength is called
monochromatic.
Radiation that spans a whole array of different
wavelengths is called continuous.
White light can be separated into a continuous spectrum
of colors.
Note that there are no dark spots on the continuous
spectrum that would correspond to different lines.
Line Spectra and the Bohr Model
Bohr Model
• Colors from excited gases arise because electrons move between energy states in
the atom. (Electronic Transition)
Line Spectra and the Bohr Model
Bohr Model
• Since the energy states are quantized, the light emitted
from excited atoms must be quantized and appear as line
spectra.
• After lots of math, Bohr showed that
 1 
En   2.178  10 18 J  2 
n 
where n is the principal quantum number (i.e., n = 1, 2, 3,
… and nothing else).
Line Spectra and the Bohr Model
Bohr Model
E  E f  Ei  hn
En   2.178  10
• We can show that
Ei  f  hn 
hc
l
  2.178  10
• When ni > nf, energy is emitted.
• When nf > ni, energy is absorbed
18
18
1 1
J  2  2 
 n f ni 
 1 
J  2 
n 
Line Spectra and
the Bohr Model
Bohr Model
Mathcad (Balmer Series)
CyberChem (Fireworks) video
Line Spectra and the Bohr Model: Balmer Series Calculations
Calculation of the first two lines in the Balmer Series for the H-atom
Balmer Series: Electronic transitions from higher E -levels (ni >2) down to the second E-level (nf=2).
 34
h  6.626 10
c  3.00 10 m s
n i  3
Red Line:
Ei.to.f
8
J s
J 

 18
2.178 10
1
 nf

2
 19
E3to2  3.025  10
6.626 10


J
1
l3to2  657.1 nm
E3to2
 19
n i  4
8
 J s  3.00 10  m s
E3to2  3.025  10
J
n f  2
J 
 18
E4to2  2.178 10
E

ni 

2
1
1 
 2  2
3 
2
l3to2 
E
h c
m
1
 34
h c
Note that:
l

J 
 18
Blue Line:
9
nm  10
n f  2
E3to2  2.178 10
l
1
1
1 
 2  2
4 
2
 19
E4to2  4.084  10
 34
l4to2 
6.626 10

8
 J s  3.00 10  m s
E4to2

J
1
l4to2  486.8 nm
Line Spectra and the Bohr Model: Balmer Series Calculations
Line Spectra and the Bohr Model
Limitations of the Bohr Model
• Can only explain the line spectrum of hydrogen
adequately.
• Can only work for (at least) one electron atoms.
• Cannot explain multi-lines with each color.
• Electrons are not completely described as small particles.
• Electrons can have both wave and particle properties.
The Wave Behavior of Matter
• Knowing that light has a particle nature, it seems
reasonable to ask if matter has a wave nature.
• Using Einstein’s and Planck’s equations, de Broglie
h
showed:
l
mv
• The momentum, mv, is a particle property, whereas l is a
wave property.
• de Broglie summarized the concepts of waves and
particles, with noticeable effects if the objects are small.
The Wave Behavior of Matter
The Uncertainty Principle
• Heisenberg’s Uncertainty Principle: on the mass scale
of atomic particles, we cannot determine exactly the
position, direction of motion, and speed simultaneously.
• For electrons: we cannot determine their momentum and
position simultaneously.
• If x is the uncertainty in position and mv is the
uncertainty in momentum, then
h
x·mv 
4
Energy and Matter
Size of Matter
Particle Property
Wave Property
Large –
macroscopic
Mainly
Unobservable
Intermediate –
electron
Some
Some
Small – photon
Few
Mainly
E = m c2
Quantum Mechanics and Atomic Orbitals
• Schrödinger proposed an equation that contains both
wave and particle terms.
^
H  E 
• Solving the equation leads to wave functions.
• The wave function gives the shape of the electronic
orbital. [“Shape” really refers to density of electronic
charges.]
• The square of the wave function, gives the probability of
finding the electron ( electron density ).
Quantum Mechanics and Atomic Orbitals
Solving Schrodinger’s
Equation gives rise to
‘Orbitals.’
These orbitals provide
the electron density
distributed about the
nucleus.
Orbitals are described
by quantum numbers.
Quantum Mechanics and Atomic Orbitals
Orbitals and Quantum Numbers
• Schrödinger’s equation requires 3 quantum numbers:
1. Principal Quantum Number, n. This is the same as Bohr’s
n. As n becomes larger, the atom becomes larger and the
electron is further from the nucleus. ( n = 1 , 2 , 3 , 4 , …. )
2. Angular Momentum Quantum Number, . This quantum
number depends on the value of n. The values of  begin at
0 and increase to (n - 1). We usually use letters for  (s, p, d
and f for  = 0, 1, 2, and 3). Usually we refer to the s, p, d
and f-orbitals.
3. Magnetic Quantum Number, m. This quantum number
depends on  . The magnetic quantum number has integral
values between -  and +  . Magnetic quantum numbers
give the 3D orientation of each orbital.