Einstein’s photo electric equation explains photo electric
effect and its further properties successfully. Wave theory of light has failed
to explain concept of photo electric effect. Hence plank’s quantum concept is
taken into consideration to explain this property. According to this property
light is emitted by a source not continuously but discreetly in the form of
wave packets called quanta.
When the light strikes a surface, number of photons are striking
the surface. More the intensity, more the number of photons. Each photon will
have certain energy, basing on the frequency of incident light. Each photon
will pass all its energy to a electron on the surface of the metal. They
electron is associated with the metal and it needs some energy to release
itself from the valency orbit.
When the energy given by the photon is sufficient to release
the electron from the metal surface, the electrons are emitted from the metal
surface. The number of the electrons emitted from the metal surface depends on
the number of the photons that are striking the metal surface. If the intensity
of the light is more, there is availability of more number of photons and hence
more photo electric current is emitted. That is the reason why intensity and
the photo electric current are proportional to each other.
The electrons in the valency orbit need a minimum energy to
get released itself from the metal surface. The incident frequency shall be
able to give at least this much of energy to release the electron. This minimum
frequency is called threshold frequency. This minimum required energy for the
release of the electron is called work function. The energy given by the photon
is first used to release the electron from the metal surface. If there is any
further energy that is given by the photon, the electron uses that energy and
moves with the kinetic energy.
According to photo electric equation, the entire energy
supplied by the photon is used first to release the electron from the metal
surface and then to move the electron from the cathode towards the anode. First
the energy has to be supplied to release the electron from the metal surface
and only when there is an extra energy it can be used to move the electron.
Supplying of energy equal to work function is the precondition for the emission
of photo electrons.
We can derive the equation for the maximum kinetic energy of
by a electron as shown below.
If intensity of light is more, more photons are available and
each photon will go and give its energy to the electrons. And hence there is
more electrons emitted and hence there will be more photo electric current. The
number of the electrons emitted is independent of frequency. But whether the
current is able to be emitted are not is a dependent of frequency. The incident
frequency and its corresponding energy shall be sufficient to release the
electron from the metal surface. That is the energy of the frequency shall be
more than the work function for the photo electric effect to happen.
Application
A monochromatic radiation incident on a metal surface of work
function W, maximum kinetic energy of the emitted electrons is K. If the
frequency of the incident radiation is n
times the initial frequency and then how its kinetic energy will be affected?
We can write photo electric equation to solve this problem.
We know that the total energy of the photon is equal to the sum of work
function and the kinetic energy of the electron. Basing on that, we can write
the equation for the kinetic energy in both the cases with their respective
frequencies as shown below. Simply buy solving this to equations we can get the
answer.
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