1000 Solved Problems in Modern Physics

244 3 Quantum Mechanics – II ∇^2 V=− 4 πZe^2 ρ whereZeis the nuclear charge andρis the charge density. ∴ f(θ)=− 8 πμ ( Ze^2 q^3 ...

3.3 Solutions 245 σ(θ)= 1 4 ( z 1 z 2 e^2 μv^2 ) 2 1 sin^4 (θ 2 ) (Rutherford scattering formula) 3.119 By Problem 3.116 F(q^2 ) ...

246 3 Quantum Mechanics – II 3.122 f(θ)=− ( μ 2 π^2 )∫ V(r)eiqrd^3 r =− ( μ 2 π^2 )∫∞ 0 V(r)r^2 dr ∫+ 1 − 1 eiqrcosθd(cosθ) ∫ ...

Chapter 4 Thermodynamics and Statistical Physics 4.1 Basic Concepts and Formulae ................................ Kinetic theory ...

248 4 Thermodynamics and Statistical Physics The Maxwell distribution N(ν)dν= 4 π ( m 2 πkT ) 3 / 2 ν^2 e−mν (^2) / 2 kT dv (4.7 ...

4.1 Basic Concepts and Formulae 249 Coefficient of diffusion (D) D= η ρ (4.13) Clausius Clepeyron equation dP dT = L T(ν 2 −ν 1 ...

250 4 Thermodynamics and Statistical Physics Thermodynamical potentials (i) Internal energy (U) (ii) Free energy (F) (iii) Gibb’ ...

4.2 Problems 251 whereWis the number of accessible states. Probability for finding a particle in thenth state at temperatureT P( ...

252 4 Thermodynamics and Statistical Physics N(α)dα= 4 N √ π α^2 e−α 2 dα where,α=ν/νpandνp=(2kT/m)^1 /^2. 4.10 Calculate the fr ...

4.2 Problems 253 4.2.2 Maxwell’s Thermodynamic Relations .............. 4.21 Obtain Maxwell’s Thermodynamic Relations (a) ( ∂s ∂ ...

254 4 Thermodynamics and Statistical Physics 4.30 Obtain the followingTdsequation Tds=CVdT+TαETdV where ET =−V (∂P ∂V ) T is the ...

4.2 Problems 255 4.42 Calculate the change of melting point of naphthalene per atmospheric change of pressure, given melting poi ...

256 4 Thermodynamics and Statistical Physics 4.54 The probability for occupying the Fermi levelPF= 1 /2. If the probability for ...

4.2 Problems 257 4.62 When the sun is directly overhead, the thermal energy incident on the earth is 1 .4kWm−^2. Assuming that t ...

258 4 Thermodynamics and Statistical Physics 4.72 Using Planck’s formula for blackbody radiation show that Stefan’s constant σ= ...

4.3 Solutions 259 of mass these two collisions appear to be equivalent so thatc′=c. We can then write f(ν 1 )f(ν 2 )=f(ν 3 )f(ν ...

260 4 Thermodynamics and Statistical Physics E= 3 NkT/ 2 (10) Combining (8), (9) and (10) α= m 2 kT (11) and A=N(α/π)^3 /^2 =N(m ...

4.3 Solutions 261 4.5 (a)νpis found by maximizing the Maxwellian distribution. d dν [ν^2 exp(−mν^2 / 2 kT)]= 0 exp(−mν^2 /kT)[2ν ...

262 4 Thermodynamics and Statistical Physics f= 4 π ( 32 × 1. 67 × 10 −^27 2 π× 1. 38 × 10 −^23 × 300 ) 3 / 2 (200)^2 exp ( − 32 ...

4.3 Solutions 263 mu− ( d dz mu ) rcosθ Let dnbe the number of molecules with velocity betweenνandν+dν per unit volume. The numb ...