# Important Notes on Modern Physics for JEE Main

Notes, Formulae and Points to be remembered or Modern Physics

**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. v
_{0}– 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 KE
_{max}Here KE_{max}= ev_{s}V_{s}– 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 10^{7} m^{-1}

for Lyman series n_{1} = 1 n_{2} = 2, 3, 4 ……………

Balmer n_{1} = 2 n_{2} = 3, 4, 5 ……………

Paschen n_{1} = 3 n_{2} = 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 = R_{0}A^{1/3}, R_{0} = 1.1 x 10^{-15} M

A – mass number

- Binding energy of nucleus of mass M, is given by B = (ZM
_{p}+ NM_{N}– M)C^{2}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 = N
_{0}e^{-}^{l}^{t}, 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 t
_{1/2}

_{}

- A radioactive nucleus can be decayed by two different phenimenas having half lives t
_{1}and t_{2}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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Neha Bagri