Practice_Midterm

Practice_Midterm - Practice Midterm Exam (Time: 90 minutes)...

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Practice Midterm Exam (Time: 90 minutes) Formulae and constants Lorentz Transormation: ! x = " ( x # vt ) ! y = y ! z = z ! t = ( t # vx / c 2 ) Inverse Lorentz Tranformation: x = ! ( " x + v " t ) y = " y z = " z t = ( " t + v " x / c 2 ) Relativistic transformation of velocities ! u x = ( u x " v ) / (1 " u x v / c 2 ) ! u y = u y / # (1 " u x v / c 2 ) Inverse Transformation: u x = ( ! u x + v ) / (1 + ! u x v / c 2 ) u y = ! u y / (1 + ! u x v / c 2 ) Relativistic Doppler Effect: f obs = 1 + v / c 1 ! v / c f source ( approaching ) Relativistic Momentum p x = mu x ; similarly for y- and z-components
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! = 1 1 " u 2 / c 2 Kinetic Energy K = mc 2 " mc 2 Total Energy E = mc 2 = K + mc 2 E 2 = p 2 c 2 + m 2 c 4 Particle of charge q moving in magnetic field B in circle of radius r has relativistic momentum p = qBr Stefan's law : et ot = σ T 4 ; et ot = power/unit area ; σ = 5.67.10 -8 W /m 2 K 4 et ot = cU /4 , U = energy density = u( λ ,T)d λ ( from 0 to ); Wien's law : λ m T = ( hc) / (4.96k B ) Rutherford scattering : Δ n = C/[(1/2 mv 2 ) 2 sin 4 ( φ /2)] e = 1.6 x 10 ! 19 C m e = 9.1 x 10 ! 31 Kg c = 3 x 10 8 m / s 1 MeV = 1.6 x 10 ! 13 J 1 MeV / c 2 = 1.78 x 10 ! 30 Kg 1 MeV / c = 5.344 x 10 ! 22 Kg . m / s Planck’s Constant h= 6.626. 10 -34 J.s =4.136. 10 -15 eV.s h = h / 2 = 1.055.10 " 34 J . s = 6.582.10 " 16 eV . s Coulomb’s constant k = 1/ (4 !" 0 ) = 8.99.10 9 N . m 2 / kg 2 Velocity of light c = 3.10 8 m/s Bohr’s quantization for Angular momentum mvr = n h Bohr radius a 0 =0.529. 10 -10 m 1 Rydberg (Energy required to ionize hydrogen atom) =13.6 eV Rydberg Constant R = 1.097. 10 7 m -1 Energy of photon E = hf For photon λ f = c Force due to Electric field : F = q E Force due to Magnetic Field: F = q
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Practice_Midterm - Practice Midterm Exam (Time: 90 minutes)...

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