Download Chapter2. Elements of quantum mechanics

Chapter2. Elements of
quantum mechanics
Present outline
Classical mechanics
1. An object in motion tends to stay in motion.
2. Force = mass times acceleration
3. For every action there is an equal and
opposite reaction.
Newton
Classical mechanics is “everyday life” mechanics.
Classical macroscopic particles
Propagating plane wave
Huygens’ principle
Propagating plane wave : Light is an Electromagnetic wave
Standing wave
Frequency content of light
Quantum mechanics: when?
1 meter
Classical mechanics
1 millimeter
Classical mechanics
1 micrometer Classical mechanics
1 nanometer
Quantum mechanics
Black body radiation
A solid object will glow or give off light if it is heated to a sufficiently high
temperature.
Figure 2.1 Wavelength dependence of the radiation
emitted by a blackbody heated to 300K, 1000K,
and 2000K. Note that the visible portion of the
spectrum is confined to wave lengths 0.4㎛
≤λ≤0.7㎛. The dashed line is the predicted
dependence for T=2000K based on classical
considerations.
Origin of quantization
The Bohr atom
Postulation by Bohr
1. Electrons exist in certain stable, circular orbits about the nucleus.
2. The electron may shift to an orbit of higher or lower energy,
thereby gaining or losing energy equal to the difference in the
energy levels.
3. The angular momentum Pθ of the electron in an orbit is always
an integral multiple of Planck’s constant divided by 2π
18/39
– The energy difference between orbits n1 and n2
Figure 2.2 Hydrogen energy levels as predicted by the Bohr theory and the
transitions corresponding to prominent, experimentally observed, spectral
lines.
– Atomic Spectra
• The analysis of absorption and emission of light by atoms
Paschen
Balmer
Lyman
λ (thousands of angstroms)
A series of sharp lines rather than a continuous distribution of
wavelengths
• Photon energy h v is related to wavelength by
•
E=h
v
= hc

∵c =
vλ
Photoelectric effect
An observation by Plank : radiation from a heated sample is emitted in discrete
units of energy, called quanta ; the energy units were described by h, where is
the frequency of the radiation, and h is a quantity called Plank’s constant
En=nhν=nћω, h = 6.63 × 10-34 J·s, ћ=h/2π
Quantization of light by Einstein → photoelectric effect
Em : a maximum energy for the emitted electrons
Em = hν - qΦ ( Φ : workfunction )
Workfunction : the minimum energy required for an electron to escape
from the metal into a vacuum
Photoelectric effect
A photoelectric experiment indicates that violet light of wavelength 420 nm is the longest
wavelength radiation that can cause photoemission of electrons from a particular
multialkali photocathode surface.
a. What is the work function of the photocathode surface, in eV?
b. If a UV radiation of wavelength 300 nm is incident upon the photocathode surface,
what will be the maximum kinetic energy of the photoemitted electrons, in eV?
c. Given that the UV light of wavelength 300 nm has an intensity of 20 mW/cm2, if the
emitted electrons are collected by applying a positive bias to the opposite electrode,
what will be the photoelectric current density in mA cm-2 ?
Solution
a. We are given max = 420 nm. The work function is then:
 = ho = hc/max = (6.626  10-34 J s)(3.0  108 m s-1)/(420  10-9 m)

 = 4.733  10-19 J or 2.96 eV
b. Given  = 300 nm, the photon energy is then:
Eph = h = hc/ = (6.626  10-34 J s)(3.0  108 m s-1)/(300  10-9 m)

Eph = 6.626  10-19 J = 4.14 eV
The kinetic energy KE of the emitted electron can then be found:
KE =  - Eph = 4.14 eV - 2.96 eV = 1.18 eV
c. The photon flux ph is the number of photons arriving per unit time per unit area. If Ilight is the light
intensity (light energy flowing through unit area per unit time) then,
ph =Ilight/Eph
Suppose that each photon creates a single electron, then
J = Charge flowing per unit area per unit time = Charge  Photon Flux

= 48.4 A m-2 = 4.84 mA cm-2
Electron impact excitation
a. A projectile electron of kinetic energy 12.2 eV collides with a hydrogen atom in a gas
discharge tube. Find the n-th energy level to which the electron in the hydrogen atom
gets excited.
b. Calculate the possible wavelengths of radiation (in nm) that will be emitted from the
excited H atom in part (a) as the electron returns to its ground state. Which one of
these wavelengths will be in the visible spectrum?
Wave - particle duality
De Broglie’s Insight
de Broglie postulated the existence of matter wa
ves. He suggested that since waves exhibit
particle-like behavior, then particles should
be expected to show wave-like properties.
de Broglie suggested that the wavelength of a
particle is expressed as  = h /p, where p
is the momentum of a particle
Wave-particle Duality
– Compton effect
E=hν=mc2,
P=mc=hν/c=h/λ
• The change in frequency and the angle corresponds exactly to
the results of a “billiard ball” collision between photon and an
electron
– De Broglie
: matter waves → wave-particle duality principle
Figure 2.3 Constructive interference of waves scattered by the
periodic atoms.
• We will use wave theory to describe the behavior of electrons in a
crystal.
Scanning electron microscope