1000 Solved Problems in Modern Physics

304 5 Solid State Physics (c)λ=vFτ=(1. 39 × 106 )(3. 7 × 10 −^14 ) = 5. 14 × 10 −^8 m 5.15 〈vD〉= e m ετ = (1. 6 × 10 −^19 )(20)( ...

5.3 Solutions 305 5.18 σ= ne^2 τ m n= 6. 02 × 1023 × 8. 88 × 106 63. 57 = 8. 38 × 1028 m−^3 σ= 8. 38 × 1028 ×(1. 6 × 10 −^19 )^2 ...

306 5 Solid State Physics Now,ρ= meVF e^2 nλ orλ= meVF ρe^2 n = (9. 11 × 10 −^31 )(1. 39 × 106 ) (1. 5 × 10 −^8 )(1. 6 × 10 −^19 ...

5.3 Solutions 307 (b) p(E)= 1 e−^1.^932 + 1 = 0. 873 (c) p(E)= 1 e^0 + 1 = 0. 5 5.28 Assuming that the Fermi energy is to be at ...

308 5 Solid State Physics (a) At high temperatures,θD>>T,orx<<1, and the exponential can be expanded to give Cv= 9 R ...

5.3 Solutions 309 N=n(E)ΔEa^3 = 1. 356 × 1028 × 0. 01 ×(10−^2 )^3 = 1. 356 × 1020 5.34 EF= h^2 8 m ( 3 n π ) 2 / 3 = (6. 63 × 10 ...

310 5 Solid State Physics 5.39 The number of silicon atoms/m^3 n= N 0 d A = 6. 02 × 1026 × 2 , 420 28 = 0. 52 × 1029 Let x be th ...

5.3 Solutions 311 5.44 I=I 0 [exp(eV/kT)−1] (1) 1 re = dI dV = eI 0 kT exp(eV/kT)(2) But exp (eV/kT)1. Therefore 1 re = eI kT o ...

312 5 Solid State Physics 5.51 f=2eV/h→V=hf/^2 e V=(6. 625 × 10 −^34 )(10^9 )/ 2 ×(1. 6 × 10 −^19 ) = 2. 07 × 10 −^6 V = 2. 07 μ ...

Chapter 6 Special Theory of Relativity 6.1 Basic Concepts and Formulae ................................ Inertial frame Laws of m ...

314 6 Special Theory of Relativity Transformation of velocities Differentiating (6.1) with respect to time and noting thatt′=tan ...

6.1 Basic Concepts and Formulae 315 Inverse transformations x=γ(x′+νt′) (6.12) y=y′ (6.13) z=z′ (6.14) t=γ ( t′+ νx′ c^2 ) (6.15 ...

316 6 Special Theory of Relativity Inverse transformations The inverse transformations (6.12), (6.13), (6.14), and (6.15) are im ...

6.1 Basic Concepts and Formulae 317 Rule: Every rigid body appears to be longest when at rest relative to the observer. When it ...

318 6 Special Theory of Relativity Inverse transformations cpx=γ(cpx′+βE′) (6.41) cpy=cp′y (6.42) cpz=cp′z (6.43) E=γ(E ′ −βcp′x ...

6.2 Problems 319 6.2 Problems.................................................. 6.2.1 LorentzTransformations.................... ...

320 6 Special Theory of Relativity 6.11 Aπ-meson with a kinetic energy of 140 MeV decays in flight intoμ-meson and a neutrino. C ...

6.2 Problems 321 6.17 If a rod is to appear shrunk by half along its direction of motion, at what speed should it travel? 6.18 A ...

322 6 Special Theory of Relativity 6.29 A spaceship is moving away from earth with speedν= 0. 6 c. When the ship is at a distanc ...

6.2 Problems 323 where the Lorentz factorγis defined as usual (ii) Hence determine the lifetime of muons at rest, knowing that w ...