{"id":174,"date":"2019-04-05T21:18:41","date_gmt":"2019-04-06T01:18:41","guid":{"rendered":"https:\/\/pressbooks.bccampus.ca\/bcitphys8400\/?post_type=chapter&p=174"},"modified":"2019-04-10T14:35:13","modified_gmt":"2019-04-10T18:35:13","slug":"chapter-2-review","status":"publish","type":"chapter","link":"https:\/\/pressbooks.bccampus.ca\/bcitphys8400\/chapter\/chapter-2-review\/","title":{"raw":"Chapter 2 Review","rendered":"Chapter 2 Review"},"content":{"raw":"
\r\n

Key Terms<\/span><\/h3>\r\n
\r\n \t
absorber<\/dt>\r\n \t
any object that absorbs radiation<\/dd>\r\n<\/dl>\r\n
\r\n \t
absorption spectrum<\/dt>\r\n \t
wavelengths of absorbed radiation by atoms and molecules<\/dd>\r\n<\/dl>\r\n
\r\n \t
Balmer formula<\/dt>\r\n \t
describes the emission spectrum of a hydrogen atom in the visible-light range<\/dd>\r\n<\/dl>\r\n
\r\n \t
Balmer series<\/dt>\r\n \t
spectral lines corresponding to electron transitions to\/from the\u00a0<\/span>n=2<\/span><\/span><\/span>\u00a0<\/span>state of the hydrogen atom, described by the Balmer formula<\/dd>\r\n<\/dl>\r\n
\r\n \t
blackbody<\/dt>\r\n \t
perfect absorber\/emitter<\/dd>\r\n<\/dl>\r\n
\r\n \t
blackbody radiation<\/dt>\r\n \t
radiation emitted by a blackbody<\/dd>\r\n<\/dl>\r\n
\r\n \t
Bohr radius of hydrogen<\/dt>\r\n \t
radius of the first Bohr\u2019s orbit<\/dd>\r\n<\/dl>\r\n
\r\n \t
Bohr\u2019s model of the hydrogen atom<\/dt>\r\n \t
first quantum model to explain emission spectra of hydrogen<\/dd>\r\n<\/dl>\r\n
\r\n \t
Brackett series<\/dt>\r\n \t
spectral lines corresponding to electron transitions to\/from the\u00a0<\/span>n=4<\/span><\/span><\/span>\u00a0<\/span>state<\/dd>\r\n<\/dl>\r\n
\r\n \t
Compton effect<\/dt>\r\n \t
the change in wavelength when an X-ray is scattered by its interaction with some materials<\/dd>\r\n<\/dl>\r\n
\r\n \t
Compton shift<\/dt>\r\n \t
difference between the wavelengths of the incident X-ray and the scattered X-ray<\/dd>\r\n<\/dl>\r\n
\r\n \t
Compton wavelength<\/dt>\r\n \t
physical constant with the value\u00a0<\/span>\u03bbc=2.43pm<\/span><\/span><\/span><\/dd>\r\n<\/dl>\r\n
\r\n \t
cut-off frequency<\/dt>\r\n \t
frequency of incident light below which the photoelectric effect does not occur<\/dd>\r\n<\/dl>\r\n
\r\n \t
cut-off wavelength<\/dt>\r\n \t
wavelength of incident light that corresponds to cut-off frequency<\/dd>\r\n<\/dl>\r\n
\r\n \t
Davisson\u2013Germer experiment<\/dt>\r\n \t
historically first electron-diffraction experiment that revealed electron waves<\/dd>\r\n<\/dl>\r\n
\r\n \t
de Broglie wave<\/dt>\r\n \t
matter wave associated with any object that has mass and momentum<\/dd>\r\n<\/dl>\r\n
\r\n \t
de Broglie\u2019s hypothesis of matter waves<\/dt>\r\n \t
particles of matter can behave like waves<\/dd>\r\n<\/dl>\r\n
\r\n \t
double-slit interference experiment<\/dt>\r\n \t
Young\u2019s double-slit experiment, which shows the interference of waves<\/dd>\r\n<\/dl>\r\n
\r\n \t
electron microscopy<\/dt>\r\n \t
microscopy that uses electron waves to \u201csee\u201d fine details of nano-size objects<\/dd>\r\n<\/dl>\r\n
\r\n \t
emission spectrum<\/dt>\r\n \t
wavelengths of emitted radiation by atoms and molecules<\/dd>\r\n<\/dl>\r\n
\r\n \t
emitter<\/dt>\r\n \t
any object that emits radiation<\/dd>\r\n<\/dl>\r\n
\r\n \t
energy of a photon<\/dt>\r\n \t
quantum of radiant energy, depends only on a photon\u2019s frequency<\/dd>\r\n<\/dl>\r\n
\r\n \t
energy spectrum of hydrogen<\/dt>\r\n \t
set of allowed discrete energies of an electron in a hydrogen atom<\/dd>\r\n<\/dl>\r\n
\r\n \t
excited energy states of the H atom<\/dt>\r\n \t
energy state other than the ground state<\/dd>\r\n<\/dl>\r\n
\r\n \t
Fraunhofer lines<\/dt>\r\n \t
dark absorption lines in the continuum solar emission spectrum<\/dd>\r\n<\/dl>\r\n
\r\n \t
ground state energy of the hydrogen atom<\/dt>\r\n \t
energy of an electron in the first Bohr orbit of the hydrogen atom<\/dd>\r\n<\/dl>\r\n
\r\n \t
group velocity<\/dt>\r\n \t
velocity of a wave, energy travels with the group velocity<\/dd>\r\n<\/dl>\r\n
\r\n \t
Heisenberg uncertainty principle<\/dt>\r\n \t
sets the limits on precision in simultaneous measurements of momentum and position of a particle<\/dd>\r\n<\/dl>\r\n
\r\n \t
Humphreys series<\/dt>\r\n \t
spectral lines corresponding to electron transitions to\/from the\u00a0<\/span>n=6<\/span><\/span><\/span>\u00a0<\/span>state<\/dd>\r\n<\/dl>\r\n
\r\n \t
hydrogen-like atom<\/dt>\r\n \t
ionized atom with one electron remaining and nucleus with charge\u00a0<\/span>+Ze<\/span><\/span><\/span><\/dd>\r\n<\/dl>\r\n
\r\n \t
inelastic scattering<\/dt>\r\n \t
scattering effect where kinetic energy is not conserved but the total energy is conserved<\/dd>\r\n<\/dl>\r\n
\r\n \t
ionization energy<\/dt>\r\n \t
energy needed to remove an electron from an atom<\/dd>\r\n<\/dl>\r\n
\r\n \t
ionization limit of the hydrogen atom<\/dt>\r\n \t
ionization energy needed to remove an electron from the first Bohr orbit<\/dd>\r\n<\/dl>\r\n
\r\n \t
Lyman series<\/dt>\r\n \t
spectral lines corresponding to electron transitions to\/from the ground state<\/dd>\r\n<\/dl>\r\n
\r\n \t
nuclear model of the atom<\/dt>\r\n \t
heavy positively charged nucleus at the center is surrounded by electrons, proposed by Rutherford<\/dd>\r\n<\/dl>\r\n
\r\n \t
Paschen series<\/dt>\r\n \t
spectral lines corresponding to electron transitions to\/from the\u00a0<\/span>n=3<\/span><\/span><\/span>\u00a0<\/span>state<\/dd>\r\n<\/dl>\r\n
\r\n \t
Pfund series<\/dt>\r\n \t
spectral lines corresponding to electron transitions to\/from the\u00a0<\/span>n=5<\/span><\/span><\/span>\u00a0<\/span>state<\/dd>\r\n<\/dl>\r\n
\r\n \t
photocurrent<\/dt>\r\n \t
in a circuit, current that flows when a photoelectrode is illuminated<\/dd>\r\n<\/dl>\r\n
\r\n \t
photoelectric effect<\/dt>\r\n \t
emission of electrons from a metal surface exposed to electromagnetic radiation of the proper frequency<\/dd>\r\n<\/dl>\r\n
\r\n \t
photoelectrode<\/dt>\r\n \t
in a circuit, an electrode that emits photoelectrons<\/dd>\r\n<\/dl>\r\n
\r\n \t
photoelectron<\/dt>\r\n \t
electron emitted from a metal surface in the presence of incident radiation<\/dd>\r\n<\/dl>\r\n
\r\n \t
photon<\/dt>\r\n \t
particle of light<\/dd>\r\n<\/dl>\r\n
\r\n \t
Planck\u2019s hypothesis of energy quanta<\/dt>\r\n \t
energy exchanges between the radiation and the walls take place only in the form of discrete energy quanta<\/dd>\r\n<\/dl>\r\n
\r\n \t
postulates of Bohr\u2019s model<\/dt>\r\n \t
three assumptions that set a frame for Bohr\u2019s model<\/dd>\r\n<\/dl>\r\n
\r\n \t
power intensity<\/dt>\r\n \t
energy that passes through a unit surface per unit time<\/dd>\r\n<\/dl>\r\n
\r\n \t
propagation vector<\/dt>\r\n \t
vector with magnitude\u00a0<\/span>2\u03c0\/\u03bb<\/span><\/span><\/span>\u00a0<\/span>that has the direction of the photon\u2019s linear momentum<\/dd>\r\n<\/dl>\r\n
\r\n \t
quantized energies<\/dt>\r\n \t
discrete energies; not continuous<\/dd>\r\n<\/dl>\r\n
\r\n \t
quantum number<\/dt>\r\n \t
index that enumerates energy levels<\/dd>\r\n<\/dl>\r\n
\r\n \t
quantum phenomenon<\/dt>\r\n \t
in interaction with matter, photon transfers either all its energy or nothing<\/dd>\r\n<\/dl>\r\n
\r\n \t
quantum state of a Planck\u2019s oscillator<\/dt>\r\n \t
any mode of vibration of Planck\u2019s oscillator, enumerated by quantum number<\/dd>\r\n<\/dl>\r\n
\r\n \t
reduced Planck\u2019s constant<\/dt>\r\n \t
Planck\u2019s constant divided by\u00a0<\/span>2\u03c0<\/span><\/span><\/span><\/dd>\r\n<\/dl>\r\n
\r\n \t
Rutherford\u2019s gold foil experiment<\/dt>\r\n \t
first experiment to demonstrate the existence of the atomic nucleus<\/dd>\r\n<\/dl>\r\n
\r\n \t
Rydberg constant for hydrogen<\/dt>\r\n \t
physical constant in the Balmer formula<\/dd>\r\n<\/dl>\r\n
\r\n \t
Rydberg formula<\/dt>\r\n \t
experimentally found positions of spectral lines of hydrogen atom<\/dd>\r\n<\/dl>\r\n
\r\n \t
scattering angle<\/dt>\r\n \t
angle between the direction of the scattered beam and the direction of the incident beam<\/dd>\r\n<\/dl>\r\n
\r\n \t
Stefan\u2013Boltzmann constant<\/dt>\r\n \t
physical constant in Stefan\u2019s law<\/dd>\r\n<\/dl>\r\n
\r\n \t
stopping potential<\/dt>\r\n \t
in a circuit, potential difference that stops photocurrent<\/dd>\r\n<\/dl>\r\n
\r\n \t
wave number<\/dt>\r\n \t
magnitude of the propagation vector<\/dd>\r\n<\/dl>\r\n
\r\n \t
wave quantum mechanics<\/dt>\r\n \t
theory that explains the physics of atoms and subatomic particles<\/dd>\r\n<\/dl>\r\n
\r\n \t
wave-particle duality<\/dt>\r\n \t
particles can behave as waves and radiation can behave as particles<\/dd>\r\n<\/dl>\r\n
\r\n \t
work function<\/dt>\r\n \t
energy needed to detach photoelectron from the metal surface<\/dd>\r\n<\/dl>\r\n
\r\n \t
\u03b1<\/span><\/span><\/span>-particle<\/dt>\r\n \t
doubly ionized helium atom<\/dd>\r\n<\/dl>\r\n
\r\n \t
\u03b1<\/span><\/span><\/span>-ray<\/dt>\r\n \t
beam of\u00a0<\/span>\u03b1<\/span><\/span><\/span>-particles (alpha-particles)<\/dd>\r\n<\/dl>\r\n
\r\n \t
\u03b2-ray<\/dt>\r\n \t
beam of electrons<\/dd>\r\n<\/dl>\r\n
\r\n \t
\u03b3-ray<\/dt>\r\n \t
beam of highly energetic photons<\/dd>\r\n<\/dl>\r\n<\/div>\r\n
\r\n

Key Equations<\/span><\/h3>\r\n
\r\n
\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n
Wien\u2019s displacement law<\/td>\r\n\u03bbmaxT=2.898\u00d710\u22123m\u22c5K<\/span><\/span><\/span><\/td>\r\n<\/tr>\r\n
Stefan\u2019s law<\/td>\r\nP(T)=\u03c3AT4<\/span><\/span><\/span><\/td>\r\n<\/tr>\r\n
Planck\u2019s constant<\/td>\r\nh=6.626\u00d710\u221234J\u22c5s=4.136\u00d710\u221215eV\u22c5s<\/span><\/span><\/span><\/td>\r\n<\/tr>\r\n
Energy quantum of radiation<\/td>\r\n\u0394E=hf<\/span><\/span><\/span><\/td>\r\n<\/tr>\r\n
Planck\u2019s blackbody radiation law<\/td>\r\nI(\u03bb,T)=2\u03c0hc2\u03bb51ehc\/\u03bbkBT\u22121<\/span><\/span><\/span><\/td>\r\n<\/tr>\r\n
Maximum kinetic energy\r\n<\/span>of a photoelectron<\/td>\r\nKmax=e\u0394Vs<\/span><\/span><\/span><\/td>\r\n<\/tr>\r\n
Energy of a photon<\/td>\r\nEf=hf<\/span><\/span><\/span><\/td>\r\n<\/tr>\r\n
Energy balance for photoelectron<\/td>\r\nKmax=hf\u2212\u03d5<\/span><\/span><\/span><\/td>\r\n<\/tr>\r\n
Cut-off frequency<\/td>\r\nfc=\u03d5h<\/span><\/span><\/span><\/td>\r\n<\/tr>\r\n
Relativistic invariant\r\n<\/span>energy equation<\/td>\r\nE2=p2c2+m02c4<\/span><\/span><\/span><\/td>\r\n<\/tr>\r\n
Energy-momentum relation\r\n<\/span>for photon<\/td>\r\npf=Efc<\/span><\/span><\/span><\/td>\r\n<\/tr>\r\n
Energy of a photon<\/td>\r\nEf=hf=hc\u03bb<\/span><\/span><\/span><\/td>\r\n<\/tr>\r\n
Magnitude of photon\u2019s momentum<\/td>\r\npf=h\u03bb<\/span><\/span><\/span><\/td>\r\n<\/tr>\r\n
Photon\u2019s linear\r\n<\/span>momentum vector<\/td>\r\np\u2192f=\u210fk\u2192<\/span><\/span><\/span><\/td>\r\n<\/tr>\r\n
The Compton wavelength\r\n<\/span>of an electron<\/td>\r\n\u03bbc=hm0c=0.00243nm<\/span><\/span><\/span><\/td>\r\n<\/tr>\r\n
The Compton shift<\/td>\r\n\u0394\u03bb=\u03bbc(1\u2212cos\u03b8)<\/span><\/span><\/span><\/td>\r\n<\/tr>\r\n
The Balmer formula<\/td>\r\n1\u03bb=RH(122\u22121n2)<\/span><\/span><\/span><\/td>\r\n<\/tr>\r\n
The Rydberg formula<\/td>\r\n1\u03bb=RH(1nf2\u22121ni2),ni=nf+1,nf+2,\u2026<\/span><\/span><\/span><\/td>\r\n<\/tr>\r\n
Bohr\u2019s first quantization condition<\/td>\r\nLn=n\u210f,n=1,2,\u2026<\/span><\/span><\/span><\/td>\r\n<\/tr>\r\n
Bohr\u2019s second quantization condition<\/td>\r\nhf=|En\u2212Em|<\/span><\/span><\/span><\/td>\r\n<\/tr>\r\n
Bohr\u2019s radius of hydrogen<\/td>\r\na0=4\u03c0\u03b50\u210f2mee2=0.529\u00c5<\/span><\/span><\/span><\/td>\r\n<\/tr>\r\n
Bohr\u2019s radius of the\u00a0<\/span>n<\/em>th orbit<\/td>\r\nrn=a0n2<\/span><\/span><\/span><\/td>\r\n<\/tr>\r\n
Ground-state energy value,\r\n<\/span>ionization limit<\/td>\r\nE0=18\u03b502mee4h2=13.6eV<\/span><\/span><\/span><\/td>\r\n<\/tr>\r\n
Electron\u2019s energy in\r\n<\/span>the\u00a0<\/span>n<\/em>th orbit<\/td>\r\nEn=\u2212E01n2<\/span><\/span><\/span><\/td>\r\n<\/tr>\r\n
Ground state energy of\r\n<\/span>hydrogen<\/td>\r\nE1=\u2212E0=\u221213.6eV<\/span><\/span><\/span><\/td>\r\n<\/tr>\r\n
The\u00a0<\/span>n<\/em>th orbit of\r\n<\/span>hydrogen-like ion<\/td>\r\nrn=a0Zn2<\/span><\/span><\/span><\/td>\r\n<\/tr>\r\n
The\u00a0<\/span>n<\/em>th energy\r\n<\/span>of hydrogen-like ion<\/td>\r\nEn=\u2212Z2E01n2<\/span><\/span><\/span><\/td>\r\n<\/tr>\r\n
Energy of a matter wave<\/td>\r\nE=hf<\/span><\/span><\/span><\/td>\r\n<\/tr>\r\n
The de Broglie wavelength<\/td>\r\n\u03bb=hp<\/span><\/span><\/span><\/td>\r\n<\/tr>\r\n
The frequency-wavelength relation\r\n<\/span>for matter waves<\/td>\r\n\u03bbf=c\u03b2<\/span><\/span><\/span><\/td>\r\n<\/tr>\r\n
Heisenberg\u2019s uncertainty principle<\/td>\r\n\u0394x\u0394p\u226512\u210f<\/span><\/span><\/span><\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\n<\/section><\/div>\r\n
\r\n

Summary<\/span><\/h3>\r\n
\r\n
\r\n

2.1<\/span>\u00a0<\/span><\/span>Blackbody Radiation<\/span><\/a><\/h4>\r\n