Important Notes on Modern Physics for JEE Main

Notes, Formulae and Points to be remembered or Modern Physics

By Neha BagriUpdated : Sep 8, 2020 , 23:17 IST
Important Notes on Modern Physics for JEE Main

Check important Modern Physics notes for JEE Main. Modern Physics is an important topic of Physics Section in JEE Main. The chapter covers at least 4-8 marks weightage in the entire JEE Main Physics Section. Below are the important points, Notes and formulae for the topic. 

Modern Physics Notes for JEE Main

Prepare the entire Modern Physics with the short notes explained below:-

Modern Physics:

  • Work function image001 λ-threshold wavelength. v0 – threshold frequency.
  • Cesium has the minimum work function which is equal to 1.9eV
  • Work function is minimum for cesium (1.9 eV)
  • Photoelectric current is directly proportional to intensity of incident radiation. (v-constant)
    I = n hv : where n = number of photons per unit area per unit time.
  • Photoelectrons ejected from the metal have kinetic energies which have range from 0 to KEmax
    Here KEmax = evs Vs – stopping potential
    So, the Stopping potential is independent of intensity of light used as V (v-constant)
  • Momentum image002 is for one photon
    The photoelectric Einstein equation is


  • Energy is given by, image004
  • The Force due to the radiation (Photon) (no transmission)

When light is incident perpendicularly

(1) image005

(2) image006

(3) Partial reflection – partial absorption


When light is incident at an angle q

(a) a = 1, r = 0


(b) r = 1, a = 0


(c) 0 < r < 1, a + r = 1


  • The expression of De Broglie wavelength is -

image011 where V → potential difference


  • Radius and speed of electron in hydrogen like atoms in the different cases is .

(i) image013

(ii) image014; Z → atomic number

;n → orbit number

(iii) image015

(iv) image016

  • Energy in the nth orbit of an atom is given by-.


  • Corresponding to spectral lines the wavelength is given by

image018 R = Rydberg constant = 1.097 x 107 m-1

for Lyman series n1 = 1 n2 = 2, 3, 4 ……………

Balmer n1 = 2 n2 = 3, 4, 5 ……………

Paschen n1 = 3 n2 = 4, 5, 6 ……………

  • Total number of possible transitions is image019 (from the nth state) [for gas having sufficient atom]
  • The Lymen series is an ultraviolet, and Paschen, Brackett and Pfund series are in the infrared region. Balmer is in visible region.
  • If effect of nucleus motion is considered,


Here m-reduced mass

image021 M-mass of nucleus

X-ray spectrum

  • Minimum wavelength for x-rays


  • Moseley's Lay


Where a and b are the positive numbers(constants) for one type of x-rays (independent of Z)

  • Average radius of nucleus may be written as

R = R0A1/3, R0 = 1.1 x 10-15 M

A – mass number

  • Binding energy of nucleus of image024 mass M, is given by B = (ZMp + NMN – M)C2 and the mass defect image025
  • For nuclear reaction A + B → C + Q

The energy of reaction Q is given by


  • α- decay process


Q-value is


Kinetic energy of a-particle is given by


  • β- decay process


  • β- decay


Where image033 are atomic masses.

  • Electron capture: where atomic electron is captured, X-ray are emitted.


Where image033 are atomic masses.

  • In radioactive decay, number of nuclei at instant t is given by N = N0 e-lt, l-decay constant.
  • Activity of sample: image035
  • Activity per unit mass is called specific activity.
  • The Half life of an nuclei is f=given by: image036
  • Number of nuclei present after n half lives i.e. after a time t = n t1/2


  • A radioactive nucleus can be decayed by two different phenimenas having half lives t1 and t2 respectively. Effective half-life of nucleus is given by image038
  • The expression for the Activity: image039
  • The Expression after n half lives is given by: image040

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Class 12thPhysics


Neha Bagri
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Neha Bagri