1000 Solved Problems in Modern Physics

284 4 Thermodynamics and Statistical Physics = e−nω/kT e−ω/kT 1 −e−ω/kT = e−nω/kT 1 eω/kT− 1 =e−nω/kT ( eω/kT−^1 ) Substi ...

4.3 Solutions 285 WhereC=constant which can be determined as follows. ΣNi=N=CΣe−βEi (11) orC= N Σe−βEi (12) Equation (10) then b ...

286 4 Thermodynamics and Statistical Physics p= 1 3 ρ<ν^2 > whereρis the mass density. In the case of photon gas, the spee ...

4.3 Solutions 287 4.67 Power radiated,P=σAT^4 = 4 πR^2 σT^4 P 2 P 1 = R^22 R^21 . T 24 T 14 = (4R 1 )^2 R^21 . (2T 1 )^4 T 14 = ...

288 4 Thermodynamics and Statistical Physics uν= 8 πν^2 c^3 kT (Rayleigh-Jeans law) (b) Ifhν/kT1 i.ehc/λkT1 then we can ignore ...

4.3 Solutions 289 = 2 15 (3.14159)^5 (1.38065)^4 × 10 −^92 (6. 626068 × 10 −^34 )^3 (2. 99792 × 108 )^2 = 5. 67 × 10 −^8 W-m−^2 ...

290 4 Thermodynamics and Statistical Physics The negative sign in (3) is omitted because asλincreasesvdecreases. 4.76 Power radi ...

Chapter 5 Solid State Physics 5.1 Basic Concepts and Formulae ................................ Crystal Structure There are seven ...

292 5 Solid State Physics The total energy of the lattice is the sum of the attractive and repulsive energies U=−NA e^2 r + b rn ...

5.1 Basic Concepts and Formulae 293 Metals, insulators and semiconductors Materials are distinguished by the extent to which the ...

294 5 Solid State Physics According to the BCS theory superconductivity is due to a weak binding of two electrons of equal and o ...

5.2 Problems 295 5.10 The energy of interaction of two atoms a distancerapart can be written as: E(r)=− a r + b r^7 whereaandbar ...

296 5 Solid State Physics 5.19 The resistivity of a certain material is 1. 72 × 10 −^8 Ωm whilst the Hall coeffi- cient is− 0. 5 ...

5.2 Problems 297 5.30 Einstein’s model of solids gives the expression for the specific heat Cv= 3 N 0 k ( θE T ) 2 eθE/T (eθE/T− ...

298 5 Solid State Physics nenh= 2. 33 × 1031 T^3 e−Eg/kT whereEgis the gap width 5.38 The effective massm∗of an electron or hole ...

5.3 Solutions 299 5.47 Given that the maximum wavelength of photon to break up Cooper pair in tin is 1. 08 × 10 −^3 m, calculate ...

300 5 Solid State Physics 5.2 Volume of the unit cell=a^3. Since there are two atoms per unit cell, 8× 1 / 8 for the corner atom ...

5.3 Solutions 301 whereEis in eV, E= ( 0. 286 λ ) 2 = ( 0. 286 1. 66 ) 2 = 0 .0297 eV. 5.7 (a)r=a/ 2 (b)r= √ 2 a/ 4 (c)r= √ 3 a/ ...

302 5 Solid State Physics 5.9 The lattice of the NaCl structure which is face-centered is represented in Fig. 5.3. The shortest ...

5.3 Solutions 303 5.11 Force,F=− dV dr = a r^2 − 7 b r^8 The particles will separate most easily when the force between them is ...