Lecture 1: Intro & Blackbody Radiation Flashcards
quantum mechanics was proposed at nearly the same time using two different but equivalent formulations:
wave mechanics
matrix mechanics
wave mechanics
following the de Broglie idea about matter waves
matrix mechanics
uses non-commutative algebra and associates to each physical quantity and physical observables a matrx
blackbody
body that totally absorbs all radiation that falls upon it
is in thermal equilibrium so also must be perfect emitter (emits across all wavelengths)
emitted radiation depends only upon
the radiator’s temperature and the total emissive power or total emittance or spctral radiance
follows stefan-boltzmann law
a typical classic model for a perfect blackbody
black cavity with a small hole
all the light entering is reflected multiple times across the black walls and is absorbed.
cavity is in thermal equilibrium, the emitted radiation depends only on its temperature so that cavity emits like a black body
stefan-boltzmann law describes the
total emittance ie the emission power per unit area at all wavelengths
the emssion spectra of black bodies depend only on
their temperature
how were physicists already aware of the shape on EM power spectrum in the 1890s
the bolometer
Wien’’s law/ Wien’s approximation/ Wien’s model
NOT Wien’s displacement law
good model for the observed spectrum at short wavelengths but is not accurate at high wavelengths
problems with the Wein’s approximation
works well at small wavelengths but not at high wavelengths
thermodynamical reasoning is not sufficient to derive an accurate model
wien’s displacement law
λmax=b/T
b= wien’s constant
T=absolute temp
Rayleight-Jeans model is based on
EM theory and standing waves
rayleigh jeans law is a good approximation to
the observed spectrum at long wavelength
big problem with the rayleigh-jeans law
the radiance keeps increasing indefinitely at short wavelengths
if it were true, the power emitted at short wavelengths would be infinite. This is the UV catastrophe
UV catastrophe
indicates the failure of classical physics to explain the behaviour of thermal radiation
outline of rayleigh-jeans derivation
start with 3D cube cavity
1. determine the numbers of modes in the cavity
2. determining the energy associated to the modes
Planck was able to derive a spectrum that fits the observed data of the blackbody spectral emission by assuming
energy comes in discrete quanta of energy
E=hv
According to the classical theory, the average energy per mode can be obtained starting from
the Maxwell-Boltxmann distribution
and using classical equipartition of energy
In classical physics the occupation of each mode was equally possible, but since modes are quantised and each quanta has energy
E=hv…
exciting higher modes is less probable because it requires more energy
he probability that a mode will be occupied is given by the
Bose-Einstein distribution function
classical: each mode needed equal energy of kbT to be excited. However, the average energy per “mode” (or “quantum”) is given by
its energy (hv) times the probability that this will be occupied
which is now dependent on frequency
why the growth of energy density at high frequencies is suppressed
the n=0 mode does not contribute to the value of <E> in Planck's spectral radiance, while in the smooth equipartition integral it is a dominant term</E>
for small hv/kbT, the discrete steps are small enough that
the distribution is pseudo-continuous: recover classical Rayleigh–Jeans form
at large hv/kbt,
the first non-zero mode is highly Boltzmann-suppressed: finite energy in the cavity - solves the ultraviolet catastrophe!
how does CMBR offer a ‘snapshot’ of universe’s structure at the time of recombination.
Photons that came from denser regions lost more energy (since they needed to give away more energy to escape from a higher gravitational attraction), making them cooler, while those from less dense regions lost less energy and appeared warmer. As a result, the temperature fluctuations in the CMB reflect the density fluctuations in the early Universe
