Photons are packets of energy emitted by a source of radiation. They travel in a straight line with speed of light. According to Planck’s quantum theory, a source of radiations wits energy in the form of photons which travel in straight line. That is the particles of light are called photons.
Energy of photon E = hv = hc / λ
H = 6.626 x 10-34 js 4.136 x 10-5 eVs
All photons travel with speed of light c = 3 x 108 ms -1 in vacuum.
Their velocity changes in the medium due to change in wavelength.
Rest mass of photon is zero, that is, photons cannot exist at rest.
Each photon has a definite energy and a definite momentum.
Energy E = hv momentum p = h/λ = mc = E/c
A photon may collide with a material particle the total energy and total momentums remain conserved in such a collision. The photon may het absorbed and / or a new photon may be emitted. Thus the number of photons may not be conserved.
The increase in intensity of light means increase in number of photons crossing a given area in a given time. The energy of each photon remains the same.
Photoelectric effect: - when light of sufficiently small wavelengths is incident on a metal surface; electrons are ejected from its surface. This phenomenon is called photoelectric effect. Electrons so emitted are called photoelectrons. Experimental setup is shown in when photos are incident on a photocathode, electrons are ejected, the anode at positive potential attracts these electrons and current is seen.
It is found experimentally is seen.
No emission occurs until the incident radiations have a frequency greater then a certain minimum called threshold frequency vo irrespective of time of exposure
No emission occurs until the incident radiations have a frequency greater then a certain minimum called threshold frequency Vo irrespective of intensity of incident radiations.
If frequency of incident radiations is greater than the threshold frequency vo then photocurrent increases on increasing the intensity
If frequency of incident radiations is greater than the threshold frequency vo then stopping potential increases if frequency of incident radiation is increased as shown in wave theory cannot explain these effects
Einstein explained this theory in 1905. He was awarded noble prize in 1921 for his contribution to explain photoelectric effect.
(KE) max = hv – hvo = hv - ∅
Max. KE of photo electrons = energy of incident radiation (photon) – work function.
Work function: - minimum energy given to electrons to bring it out of the metal is called work function. It is equivalent to ionization energy or it is the minimum energy given to an electron in its ground state of upper most filled level to transmit it to the vacuum level. It is denoted by ∅
∅ = hvo
Stopping potential: - is that negative voltage given to the anode at which photocurrent stops (becomes zero)
eVs = (KE) max
Thus eVs = hv – hvo or Vs = hv / e – hvo / e = hv / e - ∅ / e
The curve between stopping potential and frequency v (or 1 / λ ) is a straight line.
The slope is h/e if curve is between Vs and V.
The slope is hc/e if curve is between Vs and 1 / λ
Matter waves: - the wavelength of matter waves is given by de-Broglie relation and confirms the dual nature of metal.
Λ = h / p
Experiments like Davisson’s and germen’s experiment confirm wave nature of electrons. De Broglie was awarded the noble prize in 1929.
Classical mechanics works well for particles of linear size > 10-4 cm. for smaller particles quantum mechanics is to be used. Quantum mechanics take into account dual nature (wave nature and particle nature) of electrons, protons and other subatomic particles.
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