Quantum Phenomena

Photoelectric effect, electron energy levels, wave-particle duality

The Photoelectric Effect

·      Electrons are emitted from the surface of a metal when electromagnetic radiation above a certain frequency is shone on it.

-   There is no emission of electrons below the ‘threshhold frequency, fmin’ (which is different for every metal)

-   Above the threshold frequency, the numbers of electrons emitted is proportional to the intensity of radiation

-   _ = energy of a photon hitting the metal (J)
h = Plancks constant = 6.63 x 10-34Js
f = threshold  frequency (Hz)

_ = h fminThe minimum energy a photon must have to cause the emission of an electron is called the work function, _Below the threshold frequency no electrons are emitted no matter how intense the radiation

http://solarwiki.ucdavis.edu/@api/deki/files/82/=170450_46502_68.jpg

·      Wave model of light cannot explain this effect as in this theory more intense waves always carry more energy

·      The photon theory of light is required, which describes light as small packets with energy proportional to their frequency – 1 ‘packet’ of energy is 1 quanta

·      An electron is emitted from the surface when one electron in the metal absorbs one photon of light with enough energy to cause it to leave the surface

·     


Any extra energy above this minimum gives the emitted photoelectron kinetic energy:

Electron Energy Levels in Atoms

·      One consequence of quantum theory is that electrons must occupy specific energy levels in atoms

·      The lowest energy level is called the ground state

·      Excitation is when an electron moves up to a higher energy level – it requires energy to do this from either absorbing a photon or a collision with a free elctron

·     

This is similar – but not exactly the same as the electron shells you learned about in GCSE Chemistry http://www.emc.maricopa.edu/faculty/farabee/biobk/excitation.gif

Ionisation at the very topLow energy at the bottomHigh energy nearer the top
http://www.physics.udel.edu/~watson/ALLSTEL99/img004.GIF

This is a more usual way of representing energy levels in atoms in Physics – notice there are many more energy levels than the number of electrons in a normal atom of hydrogen De-excitation is when an electron moves down to a lower energy level – it emits energy as a photon of electromagnetic radiation

 

·     


Excitation can occur when a photon hits an atom but only when the energy of the photon is greater than or equal to the energy level jump of the electron

 

Fluorescent Tubes

·      Low density mercury vapour in a tube is ionized

·      Electrons in the mercury are excited as they collide with one another and with free electrons

·      The excited electrons then de-excite giving off photons with wavelengths in the UV part of the spectrum

·      These UV photons hit the inside surface of the glass tube that is coated with a fluorescent material

·      They are absorbed by electrons in the fluorescent material causing excitation

·     

http://www.ustr.net/electronics/9110hiwab.gif

These electrons then de-excite indirectly giving off photons of visible light

 


 

•	A transition between two energy levels in an atom results in a photon with a particular wavelength being emitted
•	Each line in a spectrum is caused by a particular energy level transition
•	The line spectrum is therefore a fingerprint of the energy levels in a particular element
http://astrophys-assist.com/educate/solarobs/images/spectra.gif
Spectra

 

 

 


 

Wave-Particle Duality

·      Normally we think of light as a wave – this helps to explain phenomena like diffraction

·      For effects like photo-electricity however this is not sufficient and it is useful to think of light as having a particle like nature which we call photons

·      This thinking also works in reverse. If we take an object like an electron it is usual to think of it as a particle but it also has a wave like nature. E.g. diffraction can be done with a beam of electrons

·      This dual nature of electromagnetic radiation and matter is called wave-particle duality

·      The wavelength of matter can calculated as the De-Broglie wavelength, _

_=  h/p=h/mv

_ = de Broglie wavelength (m)

h = Plancks constant = 6.63 x 10-34Js

p = momentum (kgms-1)

m = mass (kg)

v = velocity (ms-1)

 

Particles with a larger mass have a shorter de Broglie wavelength
Particles with a faster velocity have a shorter de Broglie wavelength

To do:

Describe  experiments to demonstrate the following:

 

-   The wave nature of light

 

-   The particle nature of light

 

-   The wave nature of electrons