Modern Physics is one of the most important topics from IIT-JEE mains and Advance perspective! Make sure that you go through these short notes, to score well.

### 1. CATHODE RAYS :

**(a)** Generated in a discharge tube in which a high vaccum is maintained .

**(b)** They are electrons accelerated by high p.d. ( 10 to 15 K.V.)

**(c)** K.E. of C.R. particle accelerated by a p.d. V is 1/2 mv^{2} = P^{2}/ 2m = eV.

**(d)** Can be deflected by Electric & magnetic fields.

### 2. ELECTROMAGNETIC SPECTRUM :

Ordered arrangement of the big family of electro magnetic waves (EMW) either in ascending order of frequencies or of wave lengths Speed of E.M.W. in vacuum C = 3 × 10^{8} m/s = v λ

### 3. PLANK’S QUANTUM THEORY :

A beam of EMW is a stream of discrete packets of energy called PHOTONS , each photon having a frequency v and energy = E = h v . h = plank ‘s constant = 6.63 × 10^{-34} Js .

**ALSO READ:-**

### 4. PHOTO ELECTRIC EFFECT :

The phenomenon of the emission of electrons , when metals are exposed to light (of a certain minimum frequency) is called photo electric effect.

**Results :**

**(i)** Can be explained only on the basis of the quantum theory (concept of photon) .

**(ii)** Electrons are emitted if the incident light has frequency v ≥ v_{0} (threshold frequency) emission of electrons is independent of intensity . The wave length corresponding to v_{0} is called threshold wave length λ_{0} .

**(iii)** v_{0} is different for different metals .

**(iv)** Number of electrons emitted per second depends on the intensity of the incident light .

**(v)** **EINSTEINS PHOTO ELECTRIC EQUATION** : **Photon energy = K. E. of electron + work function** .

**h** v = 1/2 mv^{2} + ϕ

ϕ = ** Work function** **= energy needed by the electron in freeing itself from the atoms of the metal** .

ϕ = **h** v_{0}

**(vi) STOPPING POTENTIAL OR CUT OFF POTENTIAL :**

The minimum value of the retarding potential to prevent electron emission is :

**eV _{cut off}** =

**(KE)**

_{max}** Note :** The number of photons incident on a surface per unit time is called photon flux.

### 5. WAVE NATURE OF MATTER :

Beams of electrons and other forms of matter exhibit wave properties including interference and diffraction with a de Broglie wave length given by λ = h/p (wave length of a praticle).

### 6. ATOMIC MODELS :

** (a) THOMSON MODEL : (PLUM PUDDING MODEL)**

**(i)** Most of the mass and all the positive charge of an atom is uniformly distributed over the full size of atom (10-10 m) .

**(ii)** Electrons are studded in this uniform distribution .

**(iii)** Failed to explain the large angle scattering α – particle scattered by thin foils of matter.

**(b) RUTHERFORD MODEL : ( Nuclear Model) **

**(i)** The most of the mass and all the positive charge is concentrated within a size of 10^{-14} m inside the atom . This concentration is called the atomic nucleus .

**(ii)** The electron revolves around the nucleus under electric interaction between them in circular orbits. An accelerating charge radiates the nucleus spiralling inward and finally fall into the nucleus , which does not happen in an atom. This could not be explained by this model .

**(c) BOHR ATOMIC MODEL :**

Bohr adopted Rutherford model of the atom & added some arbitrary conditions. These conditions are known as his postulates :

**(i)** The electron in a stable orbit does not radiate energy . i.e. mv^{2}/r = kze^{2}/ r^{2}

**(ii)** A stable orbit is that in which the angular momentum of the electron about nucleus is an integral (n) multiple of h/2π .i.e mvr = n h/2π ; n = 1 , 2 , 3 , ……. (n ≠ 0).

**(iii)** The electron can absorb or radiate energy only if the electron jumps from a lower to a higher orbit or falls from a higher to a lower orbit .

** (iv)** The energy emitted or absorbed is a light photon of frequency *v* and of energy . **E = h v**

**ALSO READ :- **

### FOR HYDROGEN ATOM : (Z = atomic number = 1)

**(i)** L_{n} = angular momentum in the n^{th} orbit = n h/2π .

**(ii)** r^{n} = radius of nth circular orbit = (0.529 A°) n^{2} ; (1A° = 10-10m) ; r_{n} α n^{2}

**(iii)** E_{n} Energy of the electron in the n^{th} orbit = -13.6 ev /n2 i.e E_{n} α 1/n^{2}

* Note : *Total energy of the electron in an atom is negative , indicating that it is bound .

Binding Energy (BE)_{n} = – E_{n} = 13.6 ev/ n^{2}

**(iv)** E_{n2} – E_{n1} = Energy emitted when an electron jumps from n_{2}^{th} orbit to n_{1}^{th } orbit (n_{2} > n_{1} ) .

ΔE = (13.6ev) [ 1/n_{1}^{2} – 1/n_{2}^{2} ].

ΔE = h*v* ; * v =* frequency of spectral line emitted* .*

1/λ = v = wave no. [no. of waves in unit length (1m)] = R [ 1/n_{1}^{2} – 1/n_{2}^{2} ]

Where R = Rydberg’s constant for hydrogen = 1.097 × 10^{7} m^{-1} .

**(v)** For hydrogen like atom/spicies of atomic number Z :

r_{nz} = Bohr radius/Z n^{2} = (0.529 A°) n^{2}/Z ; E_{nz } = (-13.6) Z^{2}/n^{2} ev

R_{2} = RZ^{2} – Rydberg’s constant for element of atomic no. Z.

### 7. SPECTRAL SERIES :

**(i) Lyman Series : **(Landing orbit n = 1) .

Ultraviolet region *V* ¯ = R [ 1/1^{2} – 1/n_{2}^{2} ] ; n^{2} > 1

**(ii) Balmer Series : **(Landing orbit n = 2)

visible region *V* ¯ = R [ 1/2^{2} – 1/ n_{2}^{2} ] ; n_{2} > 2

**(iii) Paschan Series :** (Landing orbit n = 3)

In the near infrared region *V* ¯ = R [ 1/ 3^{2} – 1/n_{2}^{2} ] ; n_{2} > 3

**(iv) Bracket Series : **(Landing orbit n = 4)

In the mid infrared region *V* ¯ = R [ 1/4^{2} – 1/ n_{2}^{2} ] ; n_{2} > 4

**(v) Pfund Series : **(Landing orbit n = 5)

In far infrared region *V* ¯ = R [ 1/5^{2} -1/n_{2}^{2} ] ; n_{2} > 5

In all these series n_{2}

= n_{1} + 1 is the α line

= n_{1} + 2 is the β line

= n_{1} + 3 is the γ line ……. etc . where n_{1} = Landing orbit

**ALSO READ:-**

Important Questions Of Complex Numbers for IIT-JEE mains and advance

### 8. EXCITATION POTENTIAL OF ATOM :

Excitation potential for quantum jump from n1 —–> n2 = E_{n2} – E_{n1} / electronch arge .

### 9. IONIZATION ENERGY :

The energy required to remove an electron from an atom . The energy required to ionize hydrogen atom is = 0 – ( – 13.6) = 13.6 ev .

### 10. IONIZATION POTENTIAL :

Potential difference through which an electron is moved to gain ionization energy = -E_{n} / electronicch arge

### 11. X – RAYS :

**(i)** Short wavelength (0.1 A° to 1A°) electromagnetic radiation .

**(ii)** Are produced when a metal anode is bombarded by very high energy electrons .

**(iii)** Are not affected by electric and magnetic field .

** (iv)** They cause photoelectric emission .

Characteristics equation eV = hνm

e = electron charge ;

V = accelerating potential

*ν*m = maximum frequency of X – radiation

**(v)** Intensity of X – rays depends on number of electrons hitting the target .

**(vi)** Cut off wavelength or minimum wavelength, where v (in volts) is the p.d. applied to the tube

λmin ≅ 12400/ v A°.

**(vii)** Continuous spectrum due to retardation of electrons .

**(viii)** Characteristic Spectrum due to transition of electron from higher to lower

### 12. NUCLEAR DIMENSIONS :

R = R_{°}A^{1/3} Where R_{°} = empirical constant = 1.1 x 10^{-15} m; A = Mass number of atom

### 13. RADIOACTIVITY :

The phenomenon of self emission of radiation is called radioactivity and the substances which emit these radiations are called radioactive substances . It can be natural or artificial (induced) .

**ALSO READ:-**

Short Notes of Complex Numbers for IIT-JEE mains and advance

### 14. α , β , γ RADIATION :

**(i)** α – particle :

**(a)** Helium nucleus (_{2}He^{4} ) ; **(b)** energy varies from 4 Mev to 9 Mev ; **(c)** Velocity 10^{6} – 10^{7} m/s ; **(d)** low penetration

** (ii)** β – particle .

**(a)** Have much less energy ; **(b)** more penetration ; **(c)** higher velocities than α particles

** (iii)** γ – radiation : Electromagnetic waves of very high energy .

### 15. LAWS OF RADIOACTIVE DISINTEGRATION :

** (A) DISPLACEMENT LAW** : In all radioactive transformation either an α or β particle (never both or more than one of each simultaneously) is emitted by the nucleus of the atom.

**(i)** α – emission : _{z}X^{A} —> _{z-2}Y^{A-4} + _{2}α^{4} + Energy

**(ii)** β – emission : _{z}X^{A} —> β + _{z+1}Y^{A} + *V* ¯ (antinuetrino)

**(iii)** γ – emission : emission does not affect either the charge number or the mass number .

**B) STASTISTICAL LAW :** The disintegration is a random phenomenon . Whcih atom disintegrates first is purely a matter of chance . Number of nuclei disintegrating per second is given ; (disintegration /s /gm is called specific activity) .

**(i)** dN/dt αN –> dN/dt = -λ = activity

where N = No.of nuclei present at time t ; λ = decay constant

**(ii)** N = N_{°} e^{-λt} N° = number of nuclei present in the beginning.

**(iii)** Half life of the population T_{1/2} = 0.693/ λ ; at the end of n half – life periods the number of nuclei left N = N_{°}/ 2^{n}

**(iv)** MEAN LIFE OF AN ATOM = ∑lifetimeof allatoms / totalnumber of atoms ; T_{av} = 1/λ

**(v)** CURIE : The unit of activity of any radioactive substance in which the number of disintegration per second is 3.7 ×10^{10} .

### 16. ATOMIC MASS UNIT ( a.m.u. OR U) :

1 amu = 1/12 x (mass of carbon – 12 atom) = 1.6603 x 10^{-27} kg

### 17. MASS AND ENERGY :

The mass m of a particle is equivalent to an energy given by E = mc^{2} ; c = speed of light . 1 amu = 931 Mev

### 18. MASS DEFECT AND BINDING ENERGY OF A NUCLEUS :

The nucleus is less massive than its constituents . The difference of masses is called mass defect

Δ M = mass defect = [ Z_{mp} + (A – Z) m_{n} – M_{za}

Total energy required to be given to the nucleus to tear apart the individual nucleons co mposing the nucleus , away from each other and beyond the range of interaction forces is called the Binding Energy of a nucleus .

B.E = (Δ M)C^{2}

B.E per nucleon = (ΔM)C^{2} / A

Greater the B.E , Greater is the stability of the nucleus.

**ALSO READ:-**

### 19. NUCLEAR FISSION :

**(i)** Heavy nuclei of A , above 200 , break up onto two or more fragments of comparable masses.

**(ii)** The total B.E. increases and excess energy is released .

**(iii)** The man point of the fission energy is leberated in the form of the K.E. ofthe fission fragments

e.g ^{235} _{92}U + _{°}n1 —> ^{236}_{92}U —> ^{141}_{56}Ba + ^{92}_{36} Kr + 3_{°}n^{1} + energy

### 20. NUCLEAR FUSION ( Thermo nuclear reaction) :

**(i)** Light nuclei of A below 20 , fuse together , the B.E. per nucleon increases and hence the excess energy is released .

**(ii)** These reactions take place at ultra high temperature ( ≅ 107 to 109)

**(iii)** Energy released exceeds the energy liberated in the fission of heavy nuclei .

e.g 4^{1}_{1} P —> ^{4}_{1}He +^{0}_{+1}e. (positron)

(iv) The energy released in fusion is specified by specifying Q value . i.e. Q value of reaction = energy released in a reaction .

Note :** (i)** In emission of β^{–} , z increases by 1.

**(ii)** In emission of β^{+} , z decreases by 1 .

## JEE Mains Crash Course offered by Eckovation

To prepare for the JEE main Exam, one needs a platform where all their problems should be solved with clear concepts. At Eckovation, you will find the following:

1. Chapter wise Notes

2. Chapter wise Practice Papers

3. Mock Tests

4. All India Test Series

5. Chapter wise Video Lectures

6. Mentors helping you at every step **(Expert Panel including IIT Delhi Graduates)**

7. Counselling

8. Peer Discussion

To Join the crash course and study with IIT Delhi Graduates: **Click Here**