Photoelectric Effect:

The emission of electrons from the surface of a cold metal when electromagnetic radiation of sufficiently high frequency is shone on it.

Threshold frequency: Minimum frequency of EM light required for electrons to be emitted from surface of metal.

Einstein’s explanation of Photoelectric effect: A beam of light consists of a stream of photons, and each photon has an energy E=hf. Intensity of the light beam is directly proportional to the number of photons passing through a unit cross-sectional area per unit time (). Light photons penetrate surface of metal plate and collide with electrons in metal:

- reflected with no change in energy

- give up all its energy to the electron

Photon does work to overcome the attractive electric forces between the electron and the ions on the metal surface. Remaining energy converted to KE of electron as it escapes.

Work function: Minimum work done to overcome attractive forces between the electron and the ions on the cold metal surface/ Minimum amount of energy required for an electron to escape from the surface of a cold metal.

Hence Einstein’s Photoelectric Equation:

In word: Photon energy = Work function energy + maximum KE of emitted photoelectrons

Planck’s constant

How does Einstein’s photoelectric theory account for threshold frequency?: The light incident on the surface consists of photons, “packets of energy”. The energy of each photon=hf where h is the Planck constant. The work function is the minimum amount of energy required to remove an electron from the surface of the metal.

Thus hf>ø,

f>ø/h

Thus there is a minimum threshold frequency below which no electrons will be emitted from the surface.

Explain why observation consistent with particle theory of light: Light energy travels in packets of energy called photons. Once the electron absorbs a photon of sufficient energy, it will be ejected from the surface. Thus does not depend on time of exposure, but rather energy and frequency of light photons.

Energy of light photon,

Photoemission Experiment (Milikan’s Verification of Einstein’s Equation):

When pd applied, no extra electrons generated, electrons emitted from cathode flow towards anode, therefore constant photocurrent[2] I detected. If anode made more negative, electrons are repelled back towards cathode as not enough KE to reach anode. Photocurrent is reduced. Anode is made increasingly negative until all the photoelectrons[3] are repelled and no current is detected. At this point pd between anode and cathode known as the stopping potential, Vs.

Hence:

Graph of eVs against frequency: , straight line graph with gradient = h, intercepts y-axis at .

Graph of photocurrent I against potential difference V applied:

Electrons are ejected only if wavelength of incident light is lower than a minimum value.

The de Broglie wavelength of the ejected electrons is NOT the same as the wavelength of the incident light.

The maximum energy of the electrons is independent of the intensity of the incident light.

The maximum energy of the electrons is dependent on the type of metal (work function).

Increasing the intensity of incident light on the emitted photoelectrons results in more light photons incident on the metal surface per second, number of photon electrons emitted per second from metal surface increases accordingly (provided photons have minimum frequency needed).

Light has a wave-particle dual nature: Acts as a wave when propagated, acts as particles when interacting with matter.

Using apparatus, find the min voltage for which the ammeter reading is zero current. The min recorded voltage is the stopping potential for the photoelectrons, and thus the max kinetic energy of the electrons in electronvolts.

De Broglie Hypothesis:

(careful do not mix this up with Einstein’s photoelectric equation!)

All moving particles have a “matter wave” associated with them. De Broglie equation gives wavelength of this matter wave/ de Broglie wavelength of a particle:

For a particle to have an observable wavelength, mass must be very small, hence only electrons and atoms exhibit observable wavelike properties.

Electron diffraction provides evidence for de Broglie’s hypothesis concerning matter waves.

Testing the de Broglie hypothesis (show wave nature of particles): Wave nature of particles shown through diffraction. Electron beam is passed through a thin film of crystalline material which acts like a diffraction grating. Wavelength of electron is the same order as the gap between the crystal atoms/atomic spacing in crystal atoms; diffraction occurs, resulting in a well-formed interference pattern similar to that of light waves.

Approximate value of atomic separation between atoms in typical crystalline solid = 10-10m

Important derivations:

Know how to use these equations to found wavelength/KE of electrons with either of the factors stated above known.

Comment on wavelength of electron in relation to size of atom: Often the order of the wavelength calculated will be similar to the size of the atom (order 10-10m), indicating that the electron energy exists as a standing wave in the atom.

Schrodinger Model/ Electron in a box:

Coloumb force binds electron to nucleus and determines energy of the electron. Electron assumed to be a wave; a wave trapped in an enclosed area becomes a standing wave, hence electron assumed to be a standing wave in the atom (exists in the potential well of the atom). Hence for electron within an atom/electron box of length L,

Wave function : Square of the amplitude of the wave function gives the probability of finding the electron at a point.

Heisenberg Uncertainty Principle:

Results from wave particle duality and unavoidable interaction between an observed object and the observer.

1) Position and momentum cannot be simultaneously measured with precision.

(When observing an electron, photon must scatter off electron enter microscope, in doing so transfers none/some/all of its momentum to the electron. Thus uncertainty in momentum of electron taken to be momentum of the photon.)

2) If an energy state only lasts for a limited time, its energy is uncertain (relation between uncertainty in time & energy).

[1] Visible light (type of EM radiation) consists of energy quanta called photons that have wave-particle duality. A photon carries an energy proportional to the radiation frequency but has zero rest mass. A photon has energy and momentum.

[2] An electric current induced by the action of light.

[3] A photoelectron is an electron emitted from an atom by interaction with a light photon.

	Created by ibukunadeleye66 over 10 years ago

Physics (Notes on Chapters) Note on WAVE NATURE OF PARTICLES (LIGHT PHOTONS[1] AND ELECTRONS), created by ibukunadeleye66 on 01/15/2014.

WAVE NATURE OF PARTICLES (LIGHT PHOTONS[1] AND ELECTRONS)