CH301 Quantum Mechanics and the Atom Notes: Part 1:.
A form of energy our eyes only detect a tiny portions of; various modern detectors ‘see’ a much
wider range. Isaac Newton sent white light through a prism - noted its a mix of many different
colors. Light behaves in many experiments as if it were a wave. Waves have known properties.
Properties of Waves - specifically Light
Waves have three linked components:
Specifically for electromagnetic waves:
For electromagnetic radiation, c = ν λ
c = speed of light = 3 x 10 m/s
What is ‘waving’?
The strength (amplitude) of both Electrical and Magnetic Fields varies: There are two waves, one
at right angles to the other, both traveling in the same direction.
The Electromagnetic Spectrum (figure in e-book is from Wikipedia)
“Light” is just a tiny section of the entire E-M spectrum. Extends in both directions.
Example: What is the frequency of green light, wavelength 520 nm?
The Electromagnetic Spectrum: what you need to know:
In addition to being able to use c = νλ, you should be able to determine for different given types
of electromagnetic radiation:
Which has the longer (bigger) wavelength?
Which has the shorter (smaller) wavelength?
Which has the highest (greatest, largest) frequency?
Which has the lowest (smallest) frequency?
Know the Visible range: 400nm-700nm (0.4-0.7μm)
Know the names of the others (not the wavelength ranges)
Know the order: (inc. wavelength) : Gamma rays, X rays, UV, Visible, IR, Microwave, Radio
Know the short wavelength (higher frequency) end of the visible is BLUER
Know the long wavelength (lower frequency) end of the visible is REDDER
Everything above absolute zero emits some E-M radiation!
A ‘Blackbody’ absorbs or emits ALL E-M radiation equally well. The relative amounts of each
wavelength emitted varies dep nding on the blackbody’s temperature.
At room temp, most of it is IR..
What happens to the coil on your electric stove, or a light bulb wire with a dimmer switch as you
turn up the power.? Hot objects appear to glow (incandescence). As temperature increases: we sense more heat (IR)
coming from the object. The object glows dull red, ten
orange, then yellow, then white.
The graph shows the resulting distribution of
intensities of different wavelengths of E-M radiation.
How does the peak and the distribution change as T
How does the area under the peak change as T
Blackbody Radiation and the UV Catastrophe
Theoreticians could NOT reproduce this experimental data. The classical mechanics model
worked poorly at long wavelengths AND predicted infinite values at short wavelengths!
“The ultraviolet catastrophe” : Any body above absolute zero would be emitting vast amounts of
UV, gamma and X-rays! The solution came with a bold jump: the assumption that energy was
QUANTIZED. Only specific amounts of energy can be absorbed or emitted by matter.
1900: Max Planck explains the emission of blackbody radiation by proposing that energy could
only be absorbed or emitted by matter in discrete “quantized” amounts, corresponding to
“packets” of energy.
The energy of a packet of light energy is related to its frequency: E = h ν where h = 6.6 x1034J.s
Cool bodies do not possess enough energy to oscillate at high frequencies so they cannot emit
UV, gamma and X-rays! This theory fits experimental data.
Another useful equation: E = (hc)/λ
What do you notice about the size of h??
Example: What is the energy of a single quanta of green light, wavelength 520nm?
More quantization evidence: The Photoelectric Effect
Shine light on a metal surface and electrons are ejected.
But ONLY if the light’s frequency is above a certain value,0ν .
For light with a frequency above ν0: Number of electrons ejected is proportional to intensity.
If the frequency of the light used is varied (e.g. using filters):
The kinetic energy of the ejected electrons increases linearly with the frequency of the light used.
Einstein Explains The Photoelectric Effect (Fig 12.8, 12.9)
Light consists of particles: photons - bundles of energy (E = hν).
A specific amount of energy Φ is needed to remove the electron from the metal atom.
This is the work function. Photons must have MORE energy than Φ .
The remaining energy shows up as kinetic (moving) energy of the electron:
KE = ½ mv e2 = hν - Φ Note Φ = hν 0 and for many metals, ν 0s in the UV.
Evidence for Wavelike Nature of Light (image from Wikipedia - under 'Young's slits') 19 thcentury: Thomas Young shows light behaves like waves, using a double-slit experiment. The
interference pattern produced was exactly that which would be made on a larger scale by water
waves. Waves interfere when they pass through one another:
CONSTRUCTIVE INTERFERENCE: Peaks, troughs coincide ("in phase"):
DESTRUCTIVE INTERFERENCE: One wave’s peak & other’s trough coincide: (out of phase)
What is Light ?
Is light a wave or a particle? There is evidence for BOTH views of light!!
1924: Prince Lois de Broglie suggests: ALL matter has a wavelike aspect to it.
It also followed that: ALL waves can behave like they are particles.
This is called WAVE PARTICLE DUALITY. Light and matter are BOTH waves AND particles!
The result we get (wave or particle) depends on how we construct an experiment!
(see the Dr. Quantum video link in Canvas for more details)
de Broglie’s Equation:
λ = h / p or λ = h / mv
Remember the size of the value of h?
The effect isn’t seen on everyday objects - they are so massive that the wavelength is infinitely
small. For particles of light, or small bits of matter like electrons, the effect is measurable.
Example: Determine the wavelength, in m, of an electron, with mass 9.11 x 10 -31 kg, having a
velocity of 50% the speed of light. Remember Planck’s constant is 6.626 x 10 -34 Js which is also
equal to 6.626 x 10-34 kg m /s.
Now determine the wavelength, in m, of a 0.22 caliber bullet, with mass 3.89 x 10-3 kg, having a
velocity of 395 m/s, ~ 1300 ft/s.
Caused by waves being scattered by points spaced at similar distances to the wavelength of the
wave. If l is known, the spacing can be found (or reverse) .
ALSO observed with electrons, neutrons etc! This fact verifies wave-particle duality! TYPES OF SPECTRA
CONTINUOUS SPECTRUM: Incandescent light source (sun, incandescent lighbulb etc.)
Pass light through a slit and then a prism (first recorded by Newton)
See the full rainbow of the visible region (the rest you cant 'see')
Pass an electric current through a pure gas sample to excite it
Send emitted light through a slit, then a prism:
ONLY certain specific wavelengths are emitted: see a series of bright lines on a dark background.
Pass white light through sample of pure gas being exited by an electric current.
Send any light that passes sample through a slit, then a prism:
ONLY certain specific wavelengths are absorbed: see a continuous spectra with dark lines.
ATOMIC SPECTRA ( also see http://astro.u-strasbg.fr/~koppen/discharge/ )
For a given element, the wavelength of the dark lines in an absorption spectra and the bright lines