Particle Nature of Light - Problem L1
We can't see objects without light.
Light helps us by making things visible.
In the night, when there is no light, we use an artificial light source to see the object and our surroundings.
That artificial light may be an electric bulb, torch, candle or any other source.
This light shows dual nature: wave nature as well as particle nature.
Light is an electromagnetic wave as predicted by Maxwell's Equations.
But, according to Einstein, light shows particle nature.
But, by the photoelectric effect, it is assumed that light is made up of a special kind of particle known as a photon.
Thus, we get introduced to this special kind of particles called photons.
Now, we will solve a problem based on the particle nature of light.
Let's solve a problem based on the particle nature of light.
Suppose we have a photon of light.
It has wavelength
$10,000$
$Angstrom$
and has an energy equal to
$1.23$
$eV$
.
When the light of wavelength
$5000$
$Angstrom$
and intensity
$I_{0}$
falls on a photoelectric cell.
Then, the saturation current becomes
$0.40×10_{−6}$
$A$
and the stopping potential becomes
$1.36$
$eV$
,
Now, we need to find the work function of that photon.
As the formula of the energy of a photon is as above.
It means the energy is inversely proportional to the wavelength as shown above.
The energy of photon
$E_{1}$
when the first radiation took place as above
The energy of photon
$E_{2}$
when the second radiation took place as above.
So, we can write this equation as above
Now, after putting the values. we get.
Hence, we get the energy of photons when the second radiation takes place.
The formula of the energy of a photon in terms of work function is given in image.
After, putting the value of
$E_{2}$
,
$V_{0}$
in given equation, we get.
Hence, we get the work function is
$1.10$
$eV$
.
The End