Lecture 1: Intro & Blackbody Radiation

Question 1

quantum mechanics was proposed at nearly the same time using two different but equivalent formulations:

Answer 1

wave mechanics

matrix mechanics

Question 2

wave mechanics

Answer 2

following the de Broglie idea about matter waves

Question 3

matrix mechanics

Answer 3

uses non-commutative algebra and associates to each physical quantity and physical observables a matrx

Question 4

blackbody

Answer 4

body that totally absorbs all radiation that falls upon it

is in thermal equilibrium so also must be perfect emitter (emits across all wavelengths)

Question 5

emitted radiation depends only upon

Answer 5

the radiator’s temperature and the total emissive power or total emittance or spctral radiance

follows stefan-boltzmann law

Question 6

a typical classic model for a perfect blackbody

Answer 6

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

Question 7

stefan-boltzmann law describes the

Answer 7

total emittance ie the emission power per unit area at all wavelengths

Question 8

the emssion spectra of black bodies depend only on

Answer 8

their temperature

Question 9

how were physicists already aware of the shape on EM power spectrum in the 1890s

Answer 9

the bolometer

Question 10

Wien’’s law/ Wien’s approximation/ Wien’s model

Answer 10

NOT Wien’s displacement law

good model for the observed spectrum at short wavelengths but is not accurate at high wavelengths

Question 11

problems with the Wein’s approximation

Answer 11

works well at small wavelengths but not at high wavelengths

thermodynamical reasoning is not sufficient to derive an accurate model

Question 12

wien’s displacement law

Answer 12

λmax=b/T

b= wien’s constant
T=absolute temp

Question 13

Rayleight-Jeans model is based on

Answer 13

EM theory and standing waves

Question 14

rayleigh jeans law is a good approximation to

Answer 14

the observed spectrum at long wavelength

Question 15

big problem with the rayleigh-jeans law

Answer 15

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

Question 16

UV catastrophe

Answer 16

indicates the failure of classical physics to explain the behaviour of thermal radiation

Question 17

outline of rayleigh-jeans derivation

Answer 17

start with 3D cube cavity
1. determine the numbers of modes in the cavity
2. determining the energy associated to the modes

Question 18

Planck was able to derive a spectrum that fits the observed data of the blackbody spectral emission by assuming

Answer 18

energy comes in discrete quanta of energy

E=hv

Question 19

According to the classical theory, the average energy per mode can be obtained starting from

Answer 19

the Maxwell-Boltxmann distribution
and using classical equipartition of energy

Question 20

In classical physics the occupation of each mode was equally possible, but since modes are quantised and each quanta has energy
E=hv…

Answer 20

exciting higher modes is less probable because it requires more energy

Question 21

he probability that a mode will be occupied is given by the

Answer 21

Bose-Einstein distribution function

Question 22

classical: each mode needed equal energy of kbT to be excited. However, the average energy per “mode” (or “quantum”) is given by

Answer 22

its energy (hv) times the probability that this will be occupied

which is now dependent on frequency

Question 23

why the growth of energy density at high frequencies is suppressed

Answer 23

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>

Question 24

for small hv/kbT, the discrete steps are small enough that

Answer 24

the distribution is pseudo-continuous: recover classical Rayleigh–Jeans form

Question 25

at large hv/kbt,

Answer 25

the first non-zero mode is highly Boltzmann-suppressed: finite energy in the cavity - solves the ultraviolet catastrophe!

Question 26

how does CMBR offer a ‘snapshot’ of universe’s structure at the time of recombination.

Answer 26

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