NEET MBBS Notes Study PG UG PDF

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📖Notes on Thermal Properties of Matter Heat:- Heat is the agent which produces in us the sensation of warmth and makes bodies hot. It is form of energy. The part of thermal energy which flows from one body to the other due to temperature difference is called heat. Nature of heat:- (a) The weight of a body remains the same weather it is heated or cooled. (b) Heat flows from higher to lower temperature (c) In any exchange of heat, heat lost by the hot body is equal to the heat gained by the cold body. (d) Substances generally expand when heated (e) A certain amount of heat known as latent heat is required to change the state of a body from solid to liquid or from liquid to gas without any change in temperature. Thermal Energy:- In accordance to dynamical theory of heat the sum total of translational, vibrational and rotational energies of the molecules of a system is called the thermal energy of the system . Unit of Heat:- (a) Calorie (cal):- It is the amount of heat required to raise the temperature of 1 gram of water through 1ºC. (b) Kilocalorie (kcal):- It is the amount of heat required to raise the temperature of 1 kilo gram of water through 1ºC. Temperature:- It is defined as the degree of hotness of a body. Zeroth Law of Thermodynamics:- It states that the two systems (A and B) which are separately in equilibrium with a third system (C) must also be in equilibrium with each other. Absoluter Zero of Temperature:- (a) Charle’s law:- Vt = V0(1+ t/273) (b) Gay Lussac’s law:- Pt = P0(1+ t/273) (c) Absolute zero of temperature is defined as the temperature at which a gas has zero volume and exerts zero pressure. It is that temperature at which molecular motion ceases. (d) C∝√T, C = √[c12 + c22 +…….+ cn2]/n Absolute gas scale or absolute scale of temperature:- It is that scale of temperature whose zero (i.e. 0ºK) = -273ºC A centigrade degree is exactly equal to the absolute or Kelvin’s degree. Conversion of temperature from one scale to another:- C/100 = (K-273)/100 = (F-32)/180 = Re/80 = (Rα-492)/180 Here C, K, F, Re and Rα are respectively, the temperatures of same both on centigrade, Kelvin, Fahrenheit, Reaumer and Rankin scale, respectively. F = [(9/5)C ]+32 K = C+273 Linear Expansion (longitudinal expansion):- When the expansion due to heating takes place only along one direction, the expansion is said to be one dimensional and linear. Coefficient of linear expansion (α):- Coefficient of linear expansion of the material of a rod is defined as the change in length per unit length, at 0ºC, per degree centigrade rise of temperature. α = lt-l0/l0t

(c) Distance of closest approach, r0 = 2Ze2/(4πε0)E Here E = ½ mv2 = KE of the α particle. Bohr’s atomic model:- (a) The central part of the atom called nucleus, contains whole of positive charge and almost whole of the mass of atom. Electrons revolve round the nucleus in fixed circular orbits. (b) Electrons are capable of revolving only in certain fixed orbits, called stationary orbits or permitted orbits. In such orbits they do not radiate any energy. (c) While revolving permitted orbit an electron possesses angular momentum L (= mvr) which is an integral multiple of h/2π. L=mvr =n (h/2π) Here n is an integer and h is the Planck’s constant. (d) Electrons are capable of changing the orbits. On absorbing energy they move to a higher orbit while emission of energy takes place when electrons move to a lower orbit. If f is the frequency of radiant energy, hf= W2-W1 Here W2 is the energy of electron in lower orbit and W1 is the energy of electron in higher orbit. (e) All the laws of mechanics can be applied to electron revolving in a stable orbit while they are not applicable to an electron in transition. Bohr’s Theory of Atom:- (a) Orbital velocity of electron:- vn= 2πkZe2/nh For a particular orbit (n= constant), orbital velocity of electron varies directly as the atomic number of the substance. vn∝Z (b) For a particular element (Z= constant), orbital velocity of the electron varies inversely as the order of the orbit. vn∝1/n (c) v = nh/2πmr Relation between vn and v1:-vn = v1/n Radius of electron:- r= n2h2/4π2kmZe2 So, r∝n2 For, C.G.S system (k = 1), r = n2h2/4π2mZe2 S.I (k = 1/4πε0), r =(ε0/π) (n2h2/mZe2) Kinetic energy of the electron:- It is the energy possessed by the electron by virtue of its motion in the orbit. K.E = ½ mv2 = ½ k (Ze2/r) Potential energy:- It is the energypossessed by the electronby virtue of its position near the nucleus. P.E = -k (Ze2/r ) Total energy:- W= K.E + P.E W=- ½ k (Ze2/r) = -k2 2π2Z2me4/n2h2 For, C.G.S (k = 1), W = - [2π2Z2me4/n2h2] For, S.I. ( k = 1/4πε0), W = - (1/8ε02) [Z2me4/n2h2] Since, W∝1/n2, a higher orbit electron possesses a lesser negative energy (greater energy) than that of a lower orbit electron. Frequency, wavelength and wave number of radiation:- Frequency, f = k2[2π2Z2me4/h3] [1/n12 – 1/n22] Wave number of radiation, Here R is the Rydberg’s constant and its value is, R= k2 [2π2Z2me4/ch3] Bohr’s theory of hydrogen atom (Z=1):- (a) Radius of orbit:- r= n2h4/4π2me2 (C.G.S) r= (ε0/π) (n2h2/me2) (S.I) (b) Energy of electron:- W= 2π2me4/n2h2 (C.G.S) W =(1/8ε0)[me4/n2h2] (c) Frequency, wavelength and wave number of radiation:- C.G.S:- k =1 and Z=1 Frequency= f=2π2me4/h3 [1/n12 – 1/n22] Wave number = 1/λ = 2π2me4/ch3 [1/n12 – 1/n22] S.I:- k =1/4πε0 and Z=1 Frequency= f = (1/8ε0) (me4/h3)[1/n12 – 1/n22] Wave number = 1/λ = (1/8ε02) (me4/ch3)[1/n12 – 1/n22] Rydberg’s constant:- R=k2 =2π2z2 me4/ch3 For hydrogen atom, Z = 1, R = RH = k2 (2π2 me4/ch3). For C.G.S system (k=1), RH = 2π2 me4/ch3 For S.I system (k=1/4πε0), RH = (1/8ε02) (me4/ch3) Wave number, 1/λ = RH [1/n12 – 1/n22] Hydrogen Spectrum:- (a) For Lyman series:- 1/λ = R [1– 1/n2], n = 2,3,4…..∞ (b) For Balmer series:- 1/λ = R [1/22 – 1/n2], n =3,4,5…..∞ (c) For Paschen series:-1/λ = R [1/32 – 1/n2], n =4,5,6…..∞ (d) For Brackett series:-1/λ = R [1/42 – 1/n2], n =5,6,7…..∞ (e) P-fund series:-1/λ = R [1/52 – 1/n2], n =6,7,8…..∞ Series limits (λmin):- (a) Lyman:- λmin = 912 Å (b) Balmer:-λmin = 3645 Å (c) Paschen:- λmin = 8201 Å Energy levels of hydrogen atom:- W = -k22π2me4/n2h2 For, n=1, W1 = -13.6 eV For the first excited state, n=2, W2 =W1/4 = (-13.6/4) eV = -3.4 eV For the second excited state, n=3, W3 =W1/9 = (-13.6/9) eV = -1.51 eV Similarly, for other excited states, W4 = -0.85 eV and W5 = -0.54 eV Number of emission lines from excited state:-n = n(n-1)/2 Ionization energy:- - E1 = +(13.6Z2)eV (a) For H-atom, I.E = 13.6 eV (b) For He+ ion, I.E = 54.4 eV (c) For Li++ ion, I.E = 122.4 eV Ionization potential:- (a) For H-atom, I.P = 13.6 eV (b) For He+ ion, I.P = 54.42 eV

🔴Revision Notes on Atomic Physics e/m of an electron (Thomson Method):- (a) e/m of a particle is called the specific charge of the particle. e/m = v/rB Here, r is the radius of curvature, B is the strength of magnetic field, v is the velocity, e is the charge on cathode ray particle and m is the mass. (b) v = E/B Electric field:- E = V/d Photo electric effect:- Photo-electric effect is the phenomenon of emission of electrons from the surfaces of certain substances, mainly metals, when light of shorter wavelength is incident upon them. Effect of collector’s potential on photoelectric current:- (a) Presence of current for zero value potential indicates that the electrons are ejected from the surface of emitter with some energy. (b) A gradual change in the number of electrons reaching the collector due to change in its potential indicates that the electrons are ejected with a variety of velocities. (c) Current is reduced to zero for some negative potential of collector indicating that there is some upper limit to the energy of electrons emitted. (d) Current depends upon the intensity of incident light. (e) Stopping potential is independent of the intensity of light. Effect of intensity of light:- The photoelectric currentis directly proportional to theintensity of incident radiation. Effect of frequency of light:- (a) Stopping potentialdepends upon thefrequency of light. Greater the frequency of light greater is the stopping potential. (b) Saturation current is independent of frequency. (c) Threshold frequency is the minimum frequency, that capable of producing photoelectric effect. Laws of Photoelectricity:- (a) Photoelectric effect is an instantaneous process. (b) Photoelectric current is directly proportional to the intensity of incident light and is independent of its frequency. (c) The stopping potential and hence the maximum velocity of the electrons depends upon the frequency of incident light and is independent of its frequency. (d) The emission of electrons stops below a certain minimum frequency known as threshold frequency. Energy contained in bundle or packet:- E = hf = hc/λ Here h is the Planck’s constant and f is the frequency. Work function:- It is defined as the minimum energy required to pull an electron out from the surface of metal. It is denoted by W0. Einstein’s equation of photoelectric effect:- (a) ½ mvmax2 = hf – W0 (b) ½ mvmax2 = hf – hf0 = h(f- f0) = h [c/λ – c/λ0] (c) eV0 = hf - W0 (d)V0 = [(h/e)f] – [W0/e] Here f0 is threshold frequency. Threshold frequency (f0):- f0 = work function/h = W/h Maximum kinetic energy of emitted photo electrons:- ?Kmax= ½ mvmax2 = eV0 Threshold wavelength:- λ0 = c/f0 = hc/hf0 = hc/W Slope of V0~ v graph:- Slope= h/e Rest mass of photon = 0, Charge = 0 Energy of photon:- E = hf = hc/λ Momentum of photon:- p = E/c = h/λ = hf/c Mass od photon:- m = E/c2 = h/cλ = hf/c2 For electron, λe = [12.27/√V]Å For proton, λp = [0.286/√V]Å For alpha particle, λα = [0.286/√V]Å For particle at temperature T, λ = h/√3mKT (E = 3/2 KT) The wavelength of electron accelerated by potential difference of V volts is:- λe= [12.27/√V]Å Number of photons:- (a) Number of photons per sec per m2, np = Intensity/hf (b) Number of photons incident per second, np = Power/hf (c) Number of electrons emitted per second = (efficiency per surface)× (number of photons incident per second) Compton wave length:- (a) λc = h/m0c Here h is the Planck’s constant, m0 is the rest mass of electron and c is the speed of light. (b) Change in wavelength:- λ' – λ =λc (1-cos?) de Broglie wavelength (λ):-λ = h/mv = h/√(2mE) = h/√(2meV) In accordance to Bohr’s postulate of atomic structure, the angular momentum of an electron is an integral multiple of h/2π. So, mvr = nh/2π Bragg’s diffraction law:- 2dsinθ = nλ Here λ is the wavelength of electron and d is distance between the planes. Rutherford’s atomic model (α-particle scattering):- (a) N(θ) ∝ cosec4(θ/2) (b) Impact parameter, b = [(Ze2) (cot θ/2)]/[(4πε0)E] Here, E = ½ mv2 = KE of theα particle.

♦️Revision Notes on Flow of Liquids and Viscosity♦️(3/3) ➖➖➖➖➖➖➖➖➖➖➖➖➖➖➖➖ Modified formula, η = [η0AT1/2]/[1+(S/T)] (b) Effect of pressure:- At low pressure, co-efficient of viscosity of a gas varies directly with pressure. Rate of flow of liquid through a liquid through a capillary tube of radius r and length l, V= πpr4/8ηl = p/(8ηl/ πr4) = p/R Here p is the pressure difference between two ends of the capillary and R is the fluid resistance. Accelerated fluid containers:- tan θ = ax/g If W be the weight of a body and U be the up thrust force of the liquid on the body then, (a) The body sinks in the liquid of W>U (b) The body floats just completely immersed if W=U Pressure exerted by a column of liquid of height h:- P = hρg Here, ρ is the density of liquid. Pressure at a point within the liquid:- P = P0 +hρg Here, P0 is the atmospheric pressure and h is the depth of point with respect to free surface of liquid.

♦️Revision Notes on Flow of Liquids and Viscosity♦️(2/3) ➖➖➖➖➖➖➖➖➖➖➖➖➖➖➖➖ Viscosity:- Viscosity is the property of fluids by virtue of which they tend to destroy any relative motion between their layers. Velocity gradient:- Velocity gradient is defined as the rate of change of velocity with respect to distance. (a) Velocity gradient = dv/dr (b) Dimension of velocity gradient = [dv/dr] = [T-1] (c) Direction of velocity gradient is perpendicular to the direction of flow, directed in the direction of increasing velocity. (d) Average velocity gradient:- Average velocity gradient is the difference between velocities of two layers separated a unit distance apart. Average velocity gradient = Δv/Δr Newton’s law of viscosity:- In accordance to Newton’s law of viscosity, the viscous drag force depends upon the nature of fluid along with following factors:- (a) F∝A (common area of two layers) (b) F∝dv/dr (velocity gradient) (c) So, F =ηA (dv/dr) Here η is called coefficient of viscosity of fluid. Coefficient of viscosity of fluid (ηv) or fugitive elasticity:- ηv = shear stress/velocity gradient = (F/A)/(dv/dr) Modulus of rigidity(ηr):- ηr = shear stress/shear strain = (F/A)/(θ) = (F/A)/(dx/dr) Here, θ = dx/dr = displacement gradient Coefficient of viscosity (Absolute viscosity or Dynamic viscosity):- F= ηA (dv/dr) if A = 1, dv = 1, dr =1, F = η Co-efficient of viscosity of a fluid is defined as the tangential force per unit area which is required to maintain (or resist) a unit relative velocity between two layers a unit distance apart. Or Co-efficient of viscosity of a fluid is defined as the tangential force per unit area which is required to maintain a unit velocity gradient between its layers. Unit of η:- S.I:- η = 1 deca poise = 1 N sec/m2 Co-efficient of viscosity of a fluid is said to be one deca-poise if a tangential force of 1 N per meter square is required to maintain a relative velocity of 1 ms-1 between its layer 1 m apart. C.G.S:- η = 1 poise = 1 dyn sec/cm2 Coefficient of viscosity of a fluid is said to be one poise if a tangential force of 1 dyn per square cm is required to maintain a relative velocity of 1 cms-1 between its layers 1 cm apart. Relation between deca-poise and poise:- 1 deca-poise = 10 poise Dimension formula for η:- η = Fdr/Adv = [M1L-1T-1] Fluidity:- Reciprocal of coefficient of viscosity of a fluid is called its fluidity. Fluidity = 1/η Unit of fluidity: poise-1 Dimension of fluidity: [M-1L1T1] Kinematic viscosity:- Kinematic viscosity of a fluid is defined as the ration between its coefficient of viscosity to the density of fluid. Kinematic viscosity = η/ρ Units of kinematic viscosity:- C.G.S – 1 stoke = cm2 s-1 Kinetic viscosity of a fluid having its dynamic viscosity one poise and density one g cm-3 is said to be 1 stoke. Dimensional formula of kinematic viscosity = η/ρ = [M0L2T-1] Critical velocity (Reynold’s Number):- Critical velocity (vc) is the maximum velocity of the flow of liquid flowing in a streamlined flow. vc = NR η/ρD Here η is the coefficient of viscosity of liquid, ρ is the density of liquid and D is the diameter of the tube. Reynold’s Number, NR = ρvcD/ η Stokes law:- In accordance to Stoke’s law, force of viscosity F depend upon, (a) Co-efficient of viscosity of fluid η (b) Radius of the moving body r (c) Velocity of body v So, force of viscosity, F = 6π η r v Terminal velocity:- v = 2/9 [r2 (ρ-σ)/η] η = 2/9 [r2 (ρ-σ)g/v] Variation of viscosity with a change in temperature and pressure:- (a) Effect of temperature:- η= A /(1+Bt)c Here A, B and C are constants. Again, ηv1/2 = Aec/vt Here, A and C are constants and v is the relative velocity. (b) Effect of pressure:- Co-efficient of viscosity of liquids increases due to an increase in pressure but there is no relation, so far, to explain the effect. Change in viscosity of gases:- (a) Effect of temperature:- Co-efficient of viscosity of a gas at a given temperature is given by, η= η0AT1/2 Here T is the absolute temperature of gas.

♦️Revision Notes on Flow of Liquids and Viscosity♦️(1/3) ➖➖➖➖➖➖➖➖➖➖➖➖➖➖➖➖ (Mechanical Properties of fluids):- Characteristic of Ideal fluid:- (a) It is incompressible (b) It is non-viscous (c) Flow of ideal fluid is irrational (d) It is capable of exhibiting steady flow Stream line flow:- Flow of a liquid fluid is said to be streamlined if the velocity of a molecule, at any point, coincides with that of the preceding one. Laminar and Turbulent FlowTube of flow:- A bundle of streamlines having same velocity of fluid elements, over any cross-section perpendicular to the direction of flow, is called a tube of flow. Laminar flow:- It is a special case of streamline flow in which velocities of all the molecules on one streamline is same throughout its motion. Turbulent flow:- Whenever the velocity of a fluid is very high or it rushes past an obstacle so that there is a sudden change in its direction of motion, the motion of fluid becomes irregular, forming eddies or whirlpools. This type of motion of fluid is called turbulent flow. Rate of flow (Equation of continuity):- Equation of Continuityav= Constant (a1v1=a2v2) Equation of continuity can be considered to be a statement of conservation of mass. So, v ∝ 1/a Velocity of flow of liquid varies inversely as the area of cross-section of the opening from where the liquid comes out. Total energy of a liquid:- (a) Kinetic energy:- It is the energy possessed by a liquid by virtue of its velocity. K.E = ½ mv2 K.E per unit mass = ½ v2 K.E per unit volume = ½ [mv2/V] = ½ ρv2 Here, ρ is the density of liquid. (b) Potential energy:- It is the energy possessed by a liquid by virtue of which of its position. Potential energy = mgh P.E per unit mass = mgh/m = gh P.E per unit volume = mgh/V = ρgh (c) Pressure energy:- It is the energy possessed by a liquid by virtue of its pressure. Pressure energy = p×V = m (p/ρ) Pressure energy per unit mass = p/ρ Pressure energy per unit volume = p×V /V= p Total energy:- Total energy of a liquid is the sum total of kinetic energy, potential energy and pressure energy. E= ½ mv2 +mgh+mp/ρ Total energy per unit mass = ½ v2 +gh+p/ρ Total energy per unit volume = ½ ρv2 +ρgh+p Bernoulli’s equation:- It states that the total energy of a small amount of an incompressible non-viscous liquid flowing without friction from one point to another, in a streamlined flow, remains constant throughout the displacement. (a) ½ mv2 + mgh+ mp/ρ = Constant (b) ½ v2 +gh+p/ρ = Constant (c) ½ ρv2 +ρgh+p = Constant or v2/2g + h + p/ρg = Constant The term v2/2g is called velocity head, h is called gravitational head and p/ρg is called pressure head. Therefore Bernoulli’s theorem states that in case of an incompressible, non-viscous fluid, flowing from one point to another in a streamlined flow, the sum total of velocity head, gravitational head and the pressure head is a constant quantity. Limitation of Bernoulli’s equation:- (a) Force of viscosity, which comes into play in case of fluids in motion has not been accounted for. (b) Loss of energy due to heat is not accounted for. (c) When a fluid flows in a curved path, the energy due to centripetal force is also not accounted for. If v is the relative velocity of top layer w.r.t. any other deeper layer (may be the lowest), then v is lesser for greater depth. v = K/bd or v ∝ 1/d Venturimeter:- It is a device used for measuring the rate of flow of liquids, generally water, through pipes. The rate of flow of water, Q = a1a2√2hg/[a12-a22] Torricelli’s theorem (velocity of efflux):- It states that the velocity of efflux of a liquid (V), from an orifice, is equal to the velocity acquired by a body, falling freely (v), from the surface of liquid to the orifice. So, V = v = √2gh

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