- In today’s article, we are going to study about ‘ What is photon and Einstein photoelectric equation? ‘ How beneficial it is and what is the wave nature of light. We will also read about some more topics like basic information about photon, De-broglie wavelength, important Numerical for examination, derivation of Einstein photoelectric equation etc in Detail. So, take your notebooks in you hand and get ready to study physics in an easy and sorted way
What is Photon?
Here are some properties write down below, by which the term photon can be easily understood.
- Photon is a elementary particle of light.
- Its energy is proportional to frequency of light.
- Photon, is neutral charged particle.
- And rest mass is zero.
E= hυ …(1)
Where h is plank’s constant.
Maxwell planks states that electron magnetic wave exchange energy in the bundle of energy. These bundle of energy is discrete. And these bundle is known as photon.
We know that υ = c/λ
Put this value in equation (1)
λ = hc/E …(2)
From Einstein mass energy relation
Hence, λ= h/p
P= h/ λ …(3)
Where P is moment.
Explanation of Einstein photoelectric equation
In 1905 Einstein use quantum theory to explain photoelectric effect. Einstein told the light has particle nature. The elementary particle of light is known as photon. It means light is travelled in bundle’s of energy. Einstein said energy of light transfer to the metal’s electron by photon. The photon’s energy is proportional to frequency of light.
E= hυ …(1)
This energy is use by a electron in two forms.
- Some part of this energy is used to escape a electron from the metal surface. This energy is equal to the work function of the metal.
- And rest of energy is converted into the kinetic energy of electron.
Work function is denoted by Φo.
Kinetic energy = E- Φo
(1/2)hυ^2 = hυ – Φo …(2)
From the equation (2) kinetic energy of electron is linearly proportional to the frequency of photon or light.
We know that (1/2)mv^2 = eυo …(3)
eυo= hυ – Φo …(4)
Note- As we know the kinetic energy of any particle should be greater than zero. If frequency is equal to the threshold frequency (υo) of metal then electron will emits from the surface of metal. But their kinetic energy is equal to zero.
0 = hυo – Φo
hυo = Φo …(5)
Put this value in equation (4) we get,
eυo= hυ – hυo …(6)
We know that υ= c/λ and υo= c/λo
Put these value in equation (6)
eυo= hc/λ – hc/λo
υo= (1/e)( hc/λ – hc/λo)
υo= ( hc/eλ – hc/eλo)
Wave nature of matter
Radiation shows particle nature as well as wave nature. De-broglie gives a hypothesis when a particle mass ‘M’ moving with velocity ‘v’ then a wavelength λ associated with this particle is given by,
λ= h/mv …(1)
This wavelength is known as De-broglie wavelength.
We know that,
mv is momentum (p)
We know that kinetic energy of a particle is,
K.E= (1/2) mv^2
And E= (1/2)mv^2
2E = mv^2
By multiplying and dividing by m,
2E = m^2 v^2 / m
2Em = m^2 v^2
2Em = P^2
P= √2Em …(3)
Put the value of P in equation (2) we get,
λ = h/ √2Em …(4)
Properties of matter waves
- Matter waves does not depend on the particle nature.
- If velocity of particle is increase then λ decreases. If v= 0 then λ is ∞. And, If v is ∞ then λ is zero.
- And If mass of particle is high the wavelength of particle is small.
Important Numerical for examination
Question 1. Find out the momentum of x-ray if its wavelength is 3A°.
Solution: λ = h/P
We have λ = 3× 10^-10 m
P= h/ λ
And, P= 6.62 × 10^-34 / 3× 10^-10 m
P= 6.62 × 10^-24 /3
P= 2.20 × 10^-24
Question 2. An electron is accelerated by 100 v potential then find out its De-broglie wavelength in term of A°.
Solution: λe = 12.27 A° / √v = 1
λe = 12.27 / √100 A°
And ,λe = 12.27/10
λe = 1.227 A°
So our article is finished and after completely reading this article, one can easily tell what is einstein photoeletric equation. And how we can explain it , what is stopping potential, threshold frequency etc.
So one can say that they got a detailed information about einstein photoelectric equation, and basic information about photon, wave nature of light, important numerical for examination, etc
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