Download The Quantum Mechanical Behavior of Light and Matter

2
1/r Laws
gravity, electric force, light
let’s look at a radiating source
same amount of energy/time, or luminosity (L)
crosses successive spheres at larger r
energy/area/time (energy flux) at distance r = L/4πr
or, luminosity/surface area
standard candles --> distances
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Lecture 3: Quantum Mechanical Behavior
of Light and Matter
wave-particle duality (eg, photoelectric effect vs. refraction)
classical: matter behaves like particles, light behaves
like waves
quantum mechanics: both matter and light behave like both
particles and waves
any formula with Planck’s constant
h = 6.63 × 10−27 gm cm2 s−1
cannot be derived from classical mechanics
Quantum Mechanical Behavior (cont.)
Photoelectric Effect (Einstein 1905)
light comes in discrete packets (photons) of energy E related
to wavelength, not intensity
=
hc
λ
Quantum Mechanical Behavior (cont.)
shorter wavelength photons have more energy, momentum
--> generate faster moving electrons
higher intensity light generates more electrons, not higher
velocity electrons
=
p = h/λ
hc
λ
Quantum Mechanical Behavior of Light
Heisenberg Uncertainty Principle
position, momentum of free particle cannot be measured to
arbitrary accuracy at same time
(∆x)(∆px ) > h
on microscopic scales, nature is fuzzy
Quantum Mechanical Behavior of Matter
p = h/λ
de Broglie (thesis!)
every particle with momentum p has associated probability wave
solutions to “particle in a
box” problem
Apply to Hydrogen Atom (Bohr’s Model)
size of electron’s orbit not arbitrary, must be integral
number of wavelengths
2πr = nλe
where λe = h/pe = h/me v
http://www.walter-fendt.de/ph11e/bohrh.htm
What are the allowable values of r?
what is v?
2
F = ma = e /r
2
2
and a = v /r for circular motion
therefore,
r = n2 (h̄/me e2 )
where h̄ = h/2π, n ≡ principal quantum number ,
h̄/me e2 ≡ Bohr radius
smallest value of r obtained from n=1 (ground state of atomic
hydrogen)
for circular orbits n = 2 has radius that is four times
larger than ground state
(even though we really mean fuzzy probability shells)
even in ground state, hydrogen atom ~ 105 bigger than its
−13
nucleus (mostly empty space)
10
electrons cannot spiral inward (in discreet shells) huge electric
forces support matter against gravity!
we really mean fuzzy probability shells
and there are
other quantum
numbers
http://www.falstad.com/qmatom/
Spectrum of Hydrogen Atom
allowable values for orbital energy of electron
E = KE + electric potential energy
2
2
= me v /2 + (−e /r)
must be quantized!
using Bohr radius
2
4
2
E = −n (me e /2h̄ )
E < 0 for bound states, E--> 0 as n--> ∞ , ionization limit
consider hydrogen atom at n’=5
electron jumps spontaneously to n=3
energy released (photon)
hc
= E n! − E n
E=
λ
photon energy fixed, characteristic
Spectrum of Hydrogen Atom (cont.)
in addition to discrete line transitions, H atom can scatter
radiation (propagation direction changes, but E, wavelength
unaffected)
make transitions to, from continuum
at n= 1, λ = 912 Å (Lyman limit) required for ionization
photons with λ > 912 Å absorbed only at discrete
wavelengths
at other wavelengths, scattered (cause of reflection and
refraction)