Modern Physics: Quick Revision of Formulae for IIT JEE, UPSEE & WBJEE

Get important formulae from unit Modern Physics for quick revision. These formulae are very useful during competitive examination. This unit includes chapters – Dual Nature of Matter and Radiation, Electronic Devices

When exams are round the corner then it is not possible to revise complete books so we have come up with unit wise formulas and important terms. Once you have gone through chapters thoroughly and understood it well there is no need to study it again and again. You can only revise important formulas and terms which will save your precious time.

In this regard find Modern Physics important Formulae for Quick Revision. These formulae will be helpful in various engineering entrance examinations such as IIT JEE, UPSEE, WBJEE etc.

In UPSEE and WBJEE where most of questions are asked directly on formulae, this quick revision note is very important.

Modern Physics

Electronic emmission

Work Function: A certain minimum amount of energy is required to be given to an electron to pull it out from the surface of the metal. This minimum energy required by an electron to escape from the metal surface is called the work function of the metal.

There are three types of electronic emissions:

(a) Thermionic emission

(b) Field emission

(c) Photo-electric emission

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Photoelectric Effect

  • All the photosensitive substances such as lithium, sodium, potassium, caesium and rubidium emit electrons when they are illuminated by light. After the discovery of electrons, these electrons were termed as photoelectrons. The phenomenon is called photoelectric effect.
  • The number of photoelectrons emitted per second is directly proportional to the intensity of incident radiation.

Einstein’s Photoelectric Equation: Energy Quantum of Radiation

  • According to Einstien: Radiation energy is built up of discrete units – the so called quanta of energy of radiation. Each quantum of radiant energy has energy hν, where h is Planck’s constant and ν the frequency of light.
  • Kmax = hν – φ0 , where φ0 is the work function of the metal

The Photon

  • E = hν      where E = photon energy, h = planck constant and ν =frequency of wave
  • p = h ν/c  where p = momentum and c = speed of light

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  • Metals: They possess very low resistivity (or high conductivity).
  • Semiconductors: They have resistivity or conductivity intermediate
  • Insulators: They have high resistivity (or low conductivity).

Intrinsic Semiconductor

  • In intrinsic semiconductors, ne = nh = ni

            where, ne = number of free electrons, nh = number of holes

            ni = intrinsic carrier concentration

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Extrinsic Semiconductor

  • When a small amount of a suitable impurity is added to the pure semiconductor to increase the conductivity, then it is called extrinsic semiconductors.
  • In n-type semiconductors, electrons become the majority carriers and holes the minority carriers, ne >> nh
  • In p-type semiconductors, the holes are the majority carriers and electrons are minority carriers,

             nh >> ne

  • The electron and hole concentration in a semiconductor in thermal equilibrium is given by,

             ne × nh = ni2

P-N Junction

  • When an external voltage V is applied across a semiconductor diode such that p-side is connected to the positive terminal of the battery and n-side to the negative terminal, it is said to be forward biased.


  • When an external voltage V is applied across the diode such that n-side is positive and p-side is negative, it is said to be reverse biased.



  • A Photodiode is a special purpose p-n junction diode fabricated with a transparent window to allow light to fall on the diode.
  • It is operated under reverse bias.
  • I-V characteristics of a photodiode for different illumination intensity

            I4 > I3 > I2 >  I1 is shown below:


Light Emitting Diode

  • It is a heavily doped p-n junction which under forward bias emits spontaneous radiation.
  • The V-I characteristics of a LED is similar to that of a Si junction diode.

Solar Cell

  • A solar cell is basically a p-n junction which generates emf when solar radiation falls on the p-n junction.
  • The I – V characteristics of solar cell is drawn in the fourth quadrant of the coordinate axes. This is because a solar cell does not draw current but supplies the same to the load.


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