Outline• Classical mechanics vs. observations (black body radiation

and Ultraviolet catastrophe)• Experiments• Photoelectric effect (experimental observations)• Max Planck’s Hypothesis• Einstein’s contributions• Photoelectric effect (explained with photons)• Properties of light• Milikan’s disbelief• Summary

Blackbody radiation• A black body absorbs and emits all frequencies of

radiation without favor.

• Blackbody radiation is the radiation emitted at different wavelengths by a heated black body, for a series of temperatures.

The ultraviolet catastrophe is the classical prediction that any black body at any temperature should emit intense ultraviolet radiation. If this were the case, Earth would be uninhabitable. Why ?

The Research History of the Photoelectric Effect

1865 Maxwell published his theory on electromagnetism. He proposed that electromagnetic waves moved at the speed of light, which led to the conclusion that light itself was a wave.

1866

•Hertz tested Maxwell’s theory by creating an electrical apparatus to detect electromagnetic radiation.

• He was able to detect radiation up to fifty feet away, and establish that the radiation was reflected, refracted, and polarized. •However, there was a limiting factor when viewing the spark created on the receiver picking up the radiation.

•Upon further investigation, Hertz was able to find that the spark was more vigorous if the receiver was exposed to ultraviolet light from the transmitter opposed to other wavelengths of visible light.

1888

•Wilhelm Hallwachs attempted to relate the phenomena with simpler conditions by investigating the action of the light on electrically charged bodies.

•He took an insulated zinc plate and attached to it a gold leaf electroscope.

•The electroscope lost its negative charge very slowly over the course of time, however, when exposed to ultraviolet light the charge leaked away very quickly.

1899•J.J. Thompson identified that ultraviolet light caused electrons to be emitted when a metallic surface was exposed to radiation in a vacuum tube.

•He also discovered that the number and the speed of the electrons emitted would be expected to vary with the intensity and the wavelength of the radiation, respectively.

1902•Lenard studied how the energy of the emitted photoelectrons varied with the intensity of the light.

•Using a carbon arc light to increase the intensity up to a thousand fold, he measured the electrons emitted from a separate metal plate on a negatively charged collector plate.

•When the electrons would make contact they would contribute to the current and show up on a sensitive ammeter to measure the current.

•The arc lamp was able to separate out the specific color wavelengths and check the photoelectric effect of each.

•The maximum energy of the ejected electron did depend on the color, the shorter the wavelength, higher the frequency light caused electrons to be ejected with more energy.

http://www.sciencejoywagon.com/physicszone/lesson/10modern/photoelc/freq.htm

Basic experiment

This is the basic set-up of the photoelectric experimentation. Light is shone on the metal and particles are ejected and the current is measured.

Photoelectric Effect: (experimental observations)

• No electrons are ejected unless the radiation has a frequency above a certain value characteristic of the metal

• Electrons are ejected immediately, however low the intensity of the radiation

• The kinetic energy, Ekin, of the ejected electrons varies

linearly with the frequency of the incident radiation

• A graph of frequency of incident radiation vs max KE of electrons from the metal has a linear slope of 6.6 x 10 –34 J/Hz This is Planck’s Constant.

Max Plank’s Hypothesis

• Proposed that the exchange of energy between matter and radiation occurs in quanta, or packets of energy

• Plank came up with E = hf to explain the observational data

• E=energy

• h=6.6 x 10-34 Planck’s constant

• f=frequency

Properties of light

The equation E=hf implies that photons of blue light are more energetic than photons of red light and that ultraviolet photons are more energetic than photons of visible light. (c=λf)

Einstein’s Contributions:

• Proposed that electromagnetic radiation consists of particles (photons).

• Each photon can be regarded as a packet of energy, and the energy of a single photon is related to the frequency of the radiation by

• Ekin   =   h f   –   W • Ekin ... maximal kinetic energy of an emitted electron • h ..... Planck constant (6.626·10-34 Js) • f ..... frequency • W ..... work function (the energy needed to free a surface

electron from a particular metal)

Stopping potential (eVstop)

• Einstein also came across the stopping potential, Vstop. When the experiments were being done, it was noticed that when raising the negative voltage on the collector plate until the current stopped, that is, to Vstop, the highest kinetic energy electrons must have had energy Vstop on leaving the cathode. Thus,

• eVstop = hf - W

• Thus Einstein's theory makes a very definite quantitative prediction: if the frequency of the incident light is varied, and Vstop plotted as a function of frequency, the slope of the line should be h/e.

Photoelectric effect:(Explained in terms of photons)

• An electron can be driven out of the metal only if it receives at least a certain minimum energy from the photon during the collision. Frequency of radiation must have a certain minimum value for electrons to be ejected

• Provided a photon has enough energy, a collision results in the immediate ejection of an electron

• If an energy Eo is needed to remove an electron from the metal and if the photon has an energy hv, then the difference hv-Eo will appear as kinetic energy of the electron. (Ekin =hf-Eo)

Milikan’s Disbelief

• Robert Milikan, an American experimental physicist would not except Einstein’s theory of energy as quanta.

• He thought it was an attack on the wave theory of light. Also, if Einstein was right, there was a completely new way to measure planck’s constant.

• He spent ten years of his life (1906-1916) working on the photoelectric effect trying to disprove Einstein.

• He even devised techniques for scraping clean the metal surface inside the vacuum tube. To his disappointment, he actual confirmed Einstein’s work with his results and measured Planck’s constant with 0.5% error. He did however earn a Nobel Prize for his series of experiments.

Example:

A)How much energy does a photon of yellow light of frequency 5.2 x 10 14 have?

A)E=hf = (6.63 x 10^-34Js) * (5.2 x 10^14Hz) = 3.4 x 10^-19J

Summary

• Studies of black-body radiation led to Planck’s hypothesis of electromagnetic radiation.

• Einstein suggestion energy as photons and developed the full equation of E = hf - W.

• Photoelectric effect was easily explained using Einstein’s Photons

• New theory was not readily excepted by scientific community, but through rigorous testing, the hypothesis was supported.

Matter waves

• Momentum of a photon is

• mv = h / lambda

• Lambda = h / mv

• DeBroglie : all matter has a wavelength

• Lambda for a baseball (m = .25 kg) leaving a bat a 20 m/s ?

Answer :

• 1.3 x 10 –34 m

• Lambda for an electron with a speed of 10 6 m/s ?

• (m of electron = 9.1 x 10 –31 kg)

answer

• 7.3 x 10 10 m

• Electron diffraction !

Exclusion Principle

No two electrons in an atom can have identical quantum numbers. This is an example of a general principle which applies not only to electrons but also to other particles of half-integer spin (fermions). It does not apply to particles of integer spin (bosons).

Virtual particles• A result of the Heisenberg Uncertainty principle is that high-

mass particles may come into being if they are incredibly short-lived. In a sense, they escape reality's notice. Such particles are called virtual particles.

• Virtual particles do not violate the conservation of energy. The kinetic energy plus mass of the initial decaying particle and the final decay products is equal. The virtual particles exist for such a short time that they can never be observed.

• Most particle processes are mediated by virtual-carrier particles. Examples include neutron beta decay, the production of charm particles, and the decay of an eta-c particle.

The uncertainty principle makes this possible . The attraction between an electron and a positron may be described as follows: the electron emits a photon with momentum directed away from the positron and thus recoils towards the positron. This entails a degree of definiteness in the momentum of the photon. There must be a corresponding uncertainty in its position - it could be on the other side of the positron so that it can hit it and knock it towards the electron .In the diagram below the wavy line represents the SAME photon.

Heisenberg's uncertainty principle is a quantitative statement of these ideas .It asserts that it is impossible to specify both the position snd the momentum of a particle.If the position is determined in the finite interval Dx and the momentum in the intervalp then these intervals obey the inequality

x.p > h / 4

so that they cannot be both reduced to zero.

Heisenberg Uncertainty Principle

• Any attempt to study the nature and motion of electrons by bombarding them with photons will change the motion and position of the electron, leading to uncertainty.