# Short Notes of Modern Physics for IIT-JEE mains and advance

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  mv2  =   P2/ 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 × 108 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 .

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### 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  ≥ v0  (threshold frequency) emission of electrons is independent of intensity . The wave length corresponding to v0 is called threshold wave length  λ0 .

(iii) v0 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  mv2  +  ϕ

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

ϕ =  h v0

(vi) STOPPING POTENTIAL OR CUT OFF POTENTIAL :

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

eVcut 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. mv2/r  =  kze2/ r2

(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 = hv

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

(i) Ln = angular momentum in the nth orbit = n h/2π .

(ii) rn = radius of nth circular orbit = (0.529 A°) n2 ; (1A° = 10-10m) ; rn α n2

(iii) En Energy of the electron in the nth orbit = -13.6 ev /n2  i.e  En  α 1/n2

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

Binding Energy (BE)n = – En = 13.6 ev/ n2

(iv) En2 – En1 = Energy emitted when an electron jumps from  n2th   orbit to  n1th   orbit  (n2 > n1 ) .

ΔE = (13.6ev)                  [   1/n12 – 1/n22  ].

ΔE = hv  ;                                    v = frequency of spectral line emitted .

1/λ =  v = wave no.    [no. of waves in unit length (1m)]   =  R  [ 1/n12 – 1/n22 ]

Where R = Rydberg’s constant for hydrogen = 1.097 × 107 m-1 .

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

rnz  =  Bohr radius/Z      n2 = (0.529 A°)  n2/Z ;  Enz  =  (-13.6)   Z2/n2 ev

R2  = RZ2  –  Rydberg’s constant for element of atomic no. Z.

### 7. SPECTRAL SERIES :

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

Ultraviolet region V ¯ = R [ 1/12 – 1/n22 ]      ;    n2 > 1

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

visible region  V ¯ =  R [ 1/22 – 1/ n22 ]              ;   n2 >  2

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

In the near infrared region  V ¯  = R [ 1/ 32 – 1/n22 ]     ;     n2 > 3

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

In the mid infrared region V ¯  = R [ 1/42 – 1/ n22 ]      ;     n2 >  4

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

In far infrared region  V ¯  = R [ 1/52 -1/n22 ]      ;   n2 >  5

In all these series n2

=  n1  +  1  is the α  line

= n1 +  2  is the β  line

= n1 +  3 is the γ  line  ……. etc .   where n1  =  Landing orbit

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### 8. EXCITATION POTENTIAL OF ATOM :

Excitation potential for quantum jump from n1 —–> n2  =  En2  – En1 / 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 =  -En / 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

νm = 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°A1/3  Where R° = empirical constant = 1.1  x   10-15 m;  A = Mass number of atom

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) .

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### 14. α , β , γ  RADIATION :

(i) α – particle :

(a) Helium nucleus (2He4 ) ;     (b) energy varies from 4 Mev to 9 Mev ;    (c) Velocity 106 – 107 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 : zXA  —> z-2YA-4 + 2α4 + Energy

(ii) β – emission : zXA   —>  β + z+1YAV ¯  (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 T1/2  = 0.693/ λ     ; at the end of n half – life periods the number of nuclei left N = N°/ 2n

(iv) MEAN LIFE OF AN ATOM =  ∑lifetimeof allatoms / totalnumber of atoms   ; Tav = 1/λ

(v) CURIE : The unit of activity of any radioactive substance in which the number of disintegration per second is                    3.7 ×1010 .

### 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 = mc2 ; 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 = [ Zmp + (A – Z) mn – Mza

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)C2

B.E per nucleon  = (ΔM)C2 / A

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

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### 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 92U + °n1 —> 23692U —> 14156Ba + 9236 Kr + 3°n1 + 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  411 P —> 41He +0+1e.  (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 .

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