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 .
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.
(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
ALSO READ :-
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
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
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) .
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+1YA + 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 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.
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 .
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)
8. Peer Discussion
To Join the crash course and study with IIT Delhi Graduates: Click Here