P114 Exam 2
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Black Body Information
- -does not have to be black
- -absorbs all radiation incident on it
- -emission of radiation is governed by its temperature
- -hot enough, radiate in visible spectrum
- -not everything black is BB, no guarentee that it will absorb raditation at all wavelengths
Interesting/Problem with Black Bodies
- - spectrum of radiation emitted by any BB at a given temp is identical, because BB's absorb all radiation, so their emission spectra is smiple.
- -b/c it;s the same, physicists could understand this spectrum by constructing a simple BB out of charge oscillators
- -more complicated BBs could be probed using the simple models.
- -Ultra-Violet Catastrophe: calculated emission spectra in theoretical BBs different with experimental observations especially at high frequency. calculations said that BBs should emit an infinite amount of radiation.
Solution to BB problem/different from classical thought
- -came up with a formula that described data well at all frequencies. explanation due to large number of charge oscillators, oscillating at different frequencies
- -energy of Planck's oscillators depended on their frequency. E=hf, h=Planck's constant. "Classical": energy of wave depended on amplitude
- -energy of Planck's oscillators had to be quantized with allowed values E=n h f, wehre n=1,2,3. only certian values of oscillator energy allowed, and oscillator had a minimum non-zero energy. "Classical": wave can have any energy that it wants.
Can't see objects in a dark room?
- -spectrum of radiation is set by its temperature
- -spectrum peaks at certain frequency (wavelength) which depends on its temperature
- -if object is at a low enough temperature, its peak emission wavelength will be below what is visible to us and amount of energy radiated in wavelengths that we could see will be small
Difference between Planck BB radiation quantized energy levels and Einstein's photon the quantum of light?
- -Planck's blackbody is an isolated case where quantization of osciallators is a special feature of the blackbody
- -Einstein's light quanta is universal. UV light from any source behaves like a particle with a specific energy according to Einstein's explanation of the photoelectric effect.
First person to see Photoelectric effect
-Hertz. He created Electromagnetic radiation by producing a spark between two electrodes. He detected radiation because another spark was produced b/n 2 electrodes in a nearby receiver. He could reduce the intensity of the receiver spark by blocking only the ultraviolet component of the transmitted radiation. UV light causes electrons to be emitted from one of the reciever electrodes. These liberated electrons increades the intensity of the sparks.
Current measured in ammeter vs the voltage on the battery
- -emitter plate at negative potential and collector at positive potential, all e- produced at emitter are accelerated toward the collector.
- -current will always flow if V=Vc-Ve is greater than zero. Positive.
- -Increasing V will not increase current, only energy of e-. To increase current, you need to increase the nubmer of electrons released by increasing the intensity of the UV light.
- -If V<0, the emitter has positive charge and the collector has negative charge. Electrons from the emitter lose enrgy if the move from the emitter to the collector. E- that start of with KE greater than amount of energy lost between emit and collect (eV) can make it to collector
- -KE of e- comes from photons and is reduced by amount of energy the lose escaping from the metal
- -Work function: minimum energy required to escape from metal plate
- -E- have max value set by enrgy of incoming photons and work function of the metal Kmax=E-W.
- -As V gets more negative , less e- have enough KE to overcome eV so current declines.
What voltage will current cease to flow?
Measure work function?
- -Kmax=E(photon)-W and E(photon)=hv
- since hv<W, the photons are no tenergetic enough to cause e- to escape and no current will flow.
- -Ecut, Kmax=Ecut-W=0
- -set the voltage on the emitter to a reasonable negative value, so that current flows in the circuit and then decrease the frequency of the incident light unti lcurrent stops flowing. gives you cutoff frequency and therefore work function.
Minimum energy of light?
Differ from Young's view of light?
- -light you see is collection of photons. the minimum energy corresponds to one photon. c/l=frequency. E=hv.
- -differs because Einstein's particle-like photons vs Young's view of light as wave-like.
- --photon has a frequency associated with it.
- --energy of photon depends only on its frequency, not on amplitude of oscillation like Young's light waves.
- --minimum energy associated with a photon of a given frequency E=hf. A classical wave or particle can have any energy it wants.
Difference between BB spectra and emission spectra of gases?
Why is it useful?
Absorption vs Emission spectrum?
See these spectra directly?
- -BB have continuous emission spectrum, they emit EM radiation at all frequencies (weak at high and low though) Gases, only emit EM radiation at a set of specific frequencies and nothing emitted in between.
- -Each element has its own emission spectrum fingerprint, unknown gasses can be identified by looking at which frequencies they emit radiation.
- -Emission spetra corresond to m raidiation that is emitted when a gas is excited in some way. The excitation moves some of the elctrons to a state of higher energy. when e- de-excites going back down to ground state it emits EM radiation ofa specific frequency. Appears as bright lines of color. Absorption is "white" light passing thoruhg a gas. e- in the gas will absorb those photons of the indicent light that have enough energy to move them to an excited state. obsever sees normal rainbow spectrum of white light with a few dark lines corresponding to frequencies at which photons are absorbed.
- -No, you need a device that spearates different frequencies of light (prism, diffraction grating).
- -Balmer noticed a very simple pattern to the spectrum of visible light emitted from hydrogen gas.
Problem with Rutherford?
How did Bohr resolve this?
Main weakness of Bohr's?
Why does energy quantization imply angular momentum quantization?
- -didn't say why all atoms have same set of orbits; why they're all identical. orbitting e- experiences an acceleration to make it move in a circle. accelerated charges radiate. e- in Hydrogen atom would radiate all of its energy and crash into the proton meaning that Hydrogen and all atoms are not stable.
- -e- only allowed to assume specific orbits around the prton. radiation emitted or absorbed when an e- moved between two fo the allowed orbits corresponds exactly to Balmer's formula for spectral lines of Hydrogen.
- -didn't know why e- didn't radiate despite the fact that they were accelerated.
- - e- in Bohr's model could only have a specific set of allowed orbits with allowed radii they could only have specific set of angular momenta.
In Hydrogen atom, transitions between which energy states lead to visible light, UV light, and infrared light?
-these types of EM radiation can be produced by transitions to a specific state n1 from any state n2>n1.
- WL range- 750 nm-1 mm
- Freq range- 4*10^14 -3*10^11 Hz
- Energy Range- 1.7-.001 eV
- Trans to n- n2=all to n1>2
- WL range- 400-750 nm
- Freq range- 7.5*10^14-4*10^14 Hz
- Energy Range-3.1-1.7 eV
- Trans to n1-n2=all to n1=n2
- WL range-4-400 nm
- Freq range-7.5*10^14-4*10^14 Hz
- Energy range-310-3.1 eV
- Trans to n1-all to n1=1
What energy photon must be absorbed by Hydro atom in lowest energy state to ionize the atom?
Can Hydro atoms be ionized by photons with higher energies than this?
What will happen if a lower energy photon is absorbed?
How would these answeres be different if light were a classical wave?
- -energy of the lowest n=1 state of hydrogen is -13.6 eV. So at least 13.6 eV of energy must be added to the H atom for its energy to be at 0. E=hf.
- -Higher energy photons can be absorbed by the atom since once the electron is free of proton its energy is no longer quantized. Excess energy above 13.6 goes towad KE of e-.
- - lower energy photon. e- of Hydro atom can only live in certain energy states. if photon has just the right energy to put e- into one of the allowed states then it can absorb the photon and jump. is its different from allowed value, e- can't use it.
- -the light's energy would not depend on the frequency if it were a wave. also, the light would not have to transfer its energy to the e- all at once. the e-'s energy would not be quantized in classical world, light of any energy could cause e-'s energy to shift.
Correspondence Principle? Different from classical
1. BB radiation
2. Bohr atom
3. Photoelectric effect
- -Classical=Quantum when kT>>hf
- Classical not =Quantum when hf> = kT. when energy of osciallator producing radiation is similar to that associated with the temperature, then quantization becomes apparent. b/c average energy of an osciallator of frequency should be kT classically. no oscillators with high frequency dominate spectrum, rship changed.
- -Classical=Quantum: large n
- Classical not = Quantum: small n
- At large state number, n, differences between a state and its neighbor n+1 are small compared to the energy of ground state (n=1). although energies are still quantized, the differences are small enough that the spectrum looks continuous. when r is large, any r is allowed. can see this in the energy diffference b/n n=1, 2 to that b/n n =1000, 1001 using the Balmer formula. only certain value of f for small n.
- - Photoelectric effect is never the same as classical, because it is inherently quantum. it doesn't matter what the photon energy is, e- are still liberated by light behaving like a particle. relevant observation , that Kmax of e- depend on hf not on intensity is true regardless of how high f becomes.
unexplanined features that de Broglie addressed
why did treating e- like a wave fix the issue?
planetary view of atom set wavelength?
- -de Broglie's matter waves addressed the fact that the electrons in the Bohr atom inhabit only specific orbits. did not directly address the question of why electrons did not radiate like other accelerated charged particles.
- -Waves involve a discrete length scale-wavelength. standing waves exist over distances that are an integral multiple of their wavelength. e- in atom are standing waves, they have specific lengths, which he related to the circumferences of their allowed orbits. e- orbiting at different radii than the allowed states are forbidden.
- -de Broglie required that an integer number of wavelengths fit around the circumference of the e- orbit. Einstein's relationship between energy and frequency of the photon he got Bohr's atom for angular momentum quantization in Hydrogen atom.
Why don't we use x-rays with photons instead of e-?
-Problem with x-rays is that it's for medical purposes, they penetrate normal matter. x-rays don't interact very strongly with matter. E- on the other hand are charged particles and therefore experience strong EM interactions with matter. advantage if you try to prove a very small sample if you want chances of the e- to interact with the sample to be high.
Sensible criterion fo an object to be quantum in nature?
-if an object's de Broglie wavelength (mass/velocity) is simiar in magnitude to its spatial exten then the object clearly cannot be treated as a classical particle. spatial extent is area over which its probability density is large. problem is "quantum" when the de Broglie wavelength of the particles is approx same order as length of scale involved in the problem. wavelength=size.
Heisenberg's view of Bohr's electron orbits?
His formulation address this view?
Physicists prefer Shroedinger?
Weakness of H and S that Dirac addressed?
- -H thought Borh's orbits were unmeasurable, not valid way to describe nature.
- -He concentrated on measurable and observable aspects like frequency of atomic emission spectra.
- -Physicists prefer S b/c it was easier to do cacluations with his wave equation and wave mechanics.
- -Neither obeyed the principle of relativistic invariance. weren't invariant under Lorentz transformations. Couldn't be used w/ problems w/ high speeds.
-Complementarity: HUP and w-p duality?
-absolute zero of temp is wehre motion ceases. incorrect why due to UP?
- -A pair of observable quantities are compmlentarity if there are limits on our ability to simultaneously determine them. W-P because wave-like and particle-like traits cannot be measured at the same time. HUP are quantitative estimates of effect of complementarity of specific pairs: momentum/position, energy/time.
- -uncertainty in the momenta of the molecules is related to uncertainty in their positions. Position is finite, so will be momentum. This contradicts the statement that molecules in an object at absolute zero are at rest. we know momenta with zero uncertainty.
-Stern Gerlach measurement/cause
-Differ from classical
-Results as evidence
- -measured the deflection of a beam of silver atoms by a non-uniform magnetic field. deflection measured by observing where silver atoms landed on a small screen a small distance away. deflection caused by field exerting a force on the atoms whose magnitude depended on direction of the angular momentum of the e- in atom with respect to direction of the mag field.
- -two distinct bands on screen, only two orientations of silver angular momentum were possible, could only certain values of deflection. different because classically the angular momentum could have any direction, all deflection possible.
- -intepreted as evidence for quantizatino of the direction of angular momentum, but actually is was evidence for spin quantum number, and the interaction of the spin angular momentum of the outermost election in silver atom with magnetic field.
Four Quantum Numbers
- -n: Energy, possible 1,2,3 integers. infinite number of values. E= -(13.6 eV)/n^2
- -l: Orbital Angular Momentum, L^2= l(l+1) h/2pi. 0,1,2, n-1, possible # of values is n.
- -m: Component of Angular Momentum Lz=m h/2 pi. possible values is -l..0..l. possible # of values is 2l+ 1.
- -ms: Component of Spin. Sz=ms h/2 pi. possible values is -1/2 and 1/2. # of values is 2.
- 2* (n^2).
-eta particle has spin zero decays to two muons, each having spin 1/3.
-Einstein and Bohr's ideas about angular momentum conservation?
- -initial angular momentumo fo the system is zero, and angular momentum conservation tells us that this value must be maintained in the final state where there are two muons. the spins of the muons must add up to zero, so they point in opposite directions.
- -Einstein-Hidden Variables: believed universe is objective and causal, and spins of each muons have objective reality independent of each other. linked by the fact that AM is conserved but detection of one is ind. of the physical existence of the other. believes there is a true theory that is objective, causal, and successful at explaining results that hasn't been found yet. the HVs preserve causality.
- -Bohr-Quantum Mechanics: believed universe is not objective and the observation of one part of the wavefunction of a system changes the state of all part. his answer to causality is that the state of muon 2 has no objective reality until we measure it. the measurement is a causal act.
-the correlation between two sets of related observations will be different in hidden variables theories and quantum mechanical theories. Hidden variables attept to preserve the objective reality of each measurement, ind. of th eother and always satisfy Bell's Inequality. Quantum theories say the entire system must be treated as a single wavefunction-measumrent on one part influence the rest and often don't satisfy Bell's Inequality. by making measurements of the correlation one can check if Bell's IEQ is satisfied or not and distinguish between HV and QM.
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