Chapter 38 Photons Electrons and Atoms About quantization
Chapter 38 Photons, Electrons, and Atoms (About quantization of light, energy and the early foundation of quantum mechanics)
Blackbody: A “perfect” absorber. For example, a hole in a cavity. It turns out a blackbody must also emit radiation, so a blackbody is not really “black”. The radiation from a blackbody depends only on the temperature of the cavity.
Blackbody Radiation The radiation from a wide variety of sources can be approximated as blackbody radiation: Coal, sun, human body (infrared) As mentioned such radiation depends only on the temperature of the object, and is sometimes refer to as thermal radiation.
Material Independence It is observed that as an object gets hotter, the predominant wavelength of the radiation emitted by the object decreases (hence the frequency increases). Example: As temperature increases: Infrared Red Yellow White This is true regardless of the material that made up the blackbody. Objects in a furnace all glow red with the furnace walls regardless of their size, shape or materials.
Temperature Dependence The peak of the wavelength distribution shifts to shorter wavelengths as the temperature increases:
Conflict with classical physics Ultraviolet catastrophe
Max Planck and Planck’s constant (1900) Proposed energy on the cavity wall: h becomes known as the Planck’s constant: All quantum calculations involves h. Sometimes it is more convenient to use:
The idea behind Planck’s equation means it is now more difficult (or energy costly) to excite a mode of higher frequency. As a result less high frequency (low wavelength) radiations are produced, preventing ultraviolet catastrophe. Classical, the cost of a high frequency mode is the same as that of a low frequency mode.
Quantization of Energy The energy emitted or absorbed by the energy transition of the cavity wall is therefore given by: The cavity cannot emit half of hf. Energy in the radiation only exists in packages (quanta) of hf.
But why hf? Even Planck himself could not give a more fundamental reason why the equation E=hf makes sense, except that it appeared to describe blackbody radiation perfectly. Planck continues to try to find a “better” explanation. Today physicists generally accept this equation as an observed fact of nature. Its introduction is regarded as the beginning of quantum mechanics.
Photoelectric Effect When light shines on certain metals, electrons are sometimes released. The emitted electrons are sometimes referred to as photoelectrons. We can measure the energy of the photoelectrons using the setup below:
The Setup When the external potential ξ is connected as shown, it helps the electrons to flow, generating a non-zero current when photoelectrons are produced.
Reversing the potential Now the external potential ξ is reversed. It actually resists the flow of the electrons. When the potential is big enough, it can even stop the current completely. This is the stopping potential Vs.
The stopping potential and the number of photoelectrons Such an experiment measures the stopping potential V , the external potential s required to stop the flow of current completely. From Vs one can deduce the maximum KE of the photoelectrons emitted by the metal, because by conservation of energy: On the other hand, the current gives a measurement of the rate of electrons released. Roughly speaking, one can say: By studying the KE and Ne of the photoelectrons, further contradictions with classical physics were found.
Photoelectric Effect, Results The maximum current increases as the intensity of the incident light increases When applied voltage is equal to or more negative than Vs, the current is zero
Photoelectric Effect Feature 1 Dependence of ejection of electrons on light frequency Classical Prediction Electrons should be ejected at any frequency as long as the light intensity is high enough Experimental Result No electrons are emitted if the incident light falls below some cutoff frequency, fc, regardless of intensity The cutoff frequency is characteristic of the material being illuminated No electrons are ejected below the cutoff frequency
Photoelectric Effect Feature 2 Dependence of photoelectron kinetic energy on light frequency Classical Prediction There should be no relationship between the frequency of the light and the electric kinetic energy The kinetic energy should be related to the intensity of the light Experimental Result The maximum kinetic energy of the photoelectrons increases with increasing light frequency
Photoelectric Effect Feature 3 Dependence of photoelectron kinetic energy on light intensity Classical Prediction Electrons should absorb energy continually from the electromagnetic waves As the light intensity incident on the metal is increased, the electrons should be ejected with more kinetic energy Experimental Result The maximum kinetic energy is independent of light intensity The current goes to zero at the same negative voltage for all intensity curves
Summary When f <fc no photoeletrons are released, independent of intensity. The cutoff frequency fc depends on the metal. Observation when f >fc : Action KE Ne Increase intensity No effects Increase frequency Increase Classical prediction for all f : Action KE Ne Increase intensity Increase frequency No effects
Frequency Dependence and Cutoff Frequency The lines show the linear relationship between KEmax and f The slope of each line is h The absolute value of the yintercept is the work function The x-intercept is the cutoff frequency This is the frequency below which no photoelectrons are emitted
Some Work Function Values
Einstein’s Explanation • Energy in light comes in packages (photons). Each photon carries energy E=hf. You cannot get half a photon or 1/3 of a photon. • The intensity of light is related to the number of photons present, but not to the frequency. • Electrons are bind to the metal, so for an electron to escape, it needs to absorb a certain threshold amount of energy ϕ, called the work function. Each metal has a different value for ϕ. The stronger the binding to the metal, the larger is ϕ.
The Picture The picture: An electron absorbs energy hf from the radiation, spends ϕ to escape from the metal, leaving only hf - ϕ as the KE: This explains why the slope of each line is h. Increase f Increase KEmax Increase intensity Increase number of e-
The cutoff frequency and wavelength
Rewriting hc
Early Models of the Atom – Rutherford Planetary model Based on results of thin foil experiments Positive charge is concentrated in the center of the atom, called the nucleus Electrons orbit the nucleus like planets orbit the sun
The trouble with the atom Maxwell’s equations says that all accelerating charge must radiate. As electrons orbits the nucleus it must also radiates continuously, hence losing energy. Result: The electron theoretically should spiral into the nucleus in a very short time (10 -8 s)… and we should all be dead.
The Bohr Theory of Hydrogen In 1913 Bohr provided an explanation of atomic spectra that includes some features of the currently accepted theory His model includes both classical and nonclassical ideas He applied Planck’s ideas of quantized energy levels to orbiting electrons In this model, the electrons are generally confined to stable, non-radiating orbits called stationary states
Energy levels Bohr’s work lead to the prediction of the existence of energy levels inside atoms. The energy of an electron when measured must lie in one of the levels, it can never possess energy between two levels. In other words, the energy between the levels are forbidden. In particular, it predicts the existence of the ground state (the lowest energy level). No energy level lies below the ground This prevents the decay of the state. electron orbit because it cannot drop below the ground state. For hydrogen:
Bohr’s Hydrogen
Terminology Ground state: n =1 First excited state: n =2 Second excited state: n =3 Ionization energy: E∞-E 1 The energy required to free an electron = For hydrogen, the ionization energy is: E∞-E 1 = 0 - (-13. 6 e. V) = 13. 6 e
Energy transition of electron
Emitting a photon Find the frequency of the photon emitted when an electron drops from n=5 to n=2.
Find the wavelength and frequency for the following transitions (n): λ f
Single electron ions other than hydrogen
Atomic spectrum
Laser Light Amplification by the Stimulated Emission of Radiation. Based on three processes: a) Absorption b) Spontaneous emission c) Stimulated emission
Stimulated Emission A photon of frequency f passes and it triggers an excited electron to fall to the lower level. Same energy, same phase, polarization, direction.
Summary
Population Inversion When there are more excited atoms than atoms at ground state, it is said to be population inverted. This can only happen when the system is not in thermal equilibrium.
He-Ne Laser Selection rules forbid He 2 s level from decaying via radiation, so a population inversion is created. It can decay via collision with Ne, hence creating a population inversion in Ne between the 5 s and 3 p levels. The decay from 5 s to 3 p is the laser beam.
- Slides: 41