# 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 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  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  is for one photon
The photoelectric Einstein equation is

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

When light is incident perpendicularly

(1)

(2)

(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 -

where V → potential difference

H-atom

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

(i)

(ii) ; Z → atomic number

;n → orbit number

(iii)

(iv)

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

• Corresponding to spectral lines the wavelength is given by

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  (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

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  mass M, is given by B = (ZMp + NMN – M)C2 and the mass defect
• 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  are atomic masses.

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

Where  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:
• Activity per unit mass is called specific activity.
• The Half life of an nuclei is f=given by:
• 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
• The expression for the Activity:
• The Expression after n half lives is given by:

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