quiz2 - PHYSICS 2D PROF. HIRSCH Formulas: QUIZ 2 SPRING...

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Unformatted text preview: PHYSICS 2D PROF. HIRSCH Formulas: QUIZ 2 SPRING QUARTER 2005 APRIL 15 2005 † † † † † Lp 1 ;g= ; c = 3 ¥ 10 8 m / s 2 2 g 1 - v /c Lorentz transformation : x ' = g ( x - vt ) ; y ' = y ; z' = z ; t ' = g ( t - vx / c 2 ) ; inverse : v Æ -v uy ux - v Velocity transformation : ux ' = ; uy ' = ; inverse : v Æ -v 2 1 - ux v / c g (1 - ux v / c 2 ) Relativistic Doppler shift : f obs = f source 1 + v / c / 1 - v / c Time dilation/length contraction : Dt = g t ; L = Momentum, energy (total, kinetic, rest) : p = g m u; E = g mc 2 ; K = (g - 1)mc 2 ; E 0 = mc 2 ; E = p 2c 2 + m 2c 4 Electron : me = 0.511 MeV / c 2 Proton : mp = 938.26 MeV / c 2 Neutron : mn = 939.55 MeV / c 2 Æ Æ Electron : me = 9.109 ¥ 10-31 kg Proton : mp = 1.673 ¥ 10-27 kg Neutron : mn = 1.675 ¥ 10-27 kg Atomic mass unit : 1 u = 931.5 MeV / c 2 electron charge = -e, proton charge = e, e = 1.6 ¥ 10 -19 C ; r r r rrr Force on charge q in E and B fields : F = q( E + v ¥ B) ; centripetal acceleration = v 2 / R • Stefan' s law : R = sT 4 , R = power/unit area ; s = 5.67 ¥ 10-8 W / m 2K 4 ; R = cU / 4 , U = energy density = † Ú u(l)dl 0 † † † † † 8p hc / l hc Planck' s law : u( l, T ) = n ( l) ¥ e ( l, T ) = 4 ¥ hc / lkT ; Wien' s law : lm T = l e -1 4.96 k 12 Photoelectric effect : eV0 = ( mv ) max = hf - f , f ≡ work function 2 Constants : h = 4.136 ¥ 10-15 eV ⋅ s ; hc = 12, 400 eV A ; k = 1 /11, 600 eV/K Justify all your answers to all problems Problem 1 (15 points) direction of emerging beam 900 protons region of uniform B-field d=1.5m A beam of protons moving at uniform speed in the plane of the paper in the horizontal direction enters a region of extension d=1.5m in the horizontal direction and infinite in the vertical direction, where a uniform magnetic field of magnitude B=0.05T exists. The beam emerges still in the plane of the paper at a 900 angle from the horizontal direction pointing upwards as shown in the figure. (a) In which direction does the magnetic field point? (b) What is the speed of the protons in m/s? mass of proton mp =1.67x10-27kg (c) How long (in s) does it take a proton to traverse the region of B-field? PHYSICS 2D PROF. HIRSCH QUIZ 2 SPRING QUARTER 2005 APRIL 15 2005 Problem 2 (15 points) According to classical physics, the average energy in a mode of oscillation is kT, independent of wavelength. For a cavity at temperature T=3000K: (a) What is the average energy in a mode according to classical physics, in eV? (b) Find two values of the wavelength l, that are different by at least a factor of 5, for which the classical result found in (a) is in error by less than 10%. Give the value of the average energy (in eV) for one of them. (c) Find a value of the wavelength for which the classical result in (a) is in error by a factor of 1000 or more. Give the correct average energy for that wavelength. (d) For l=10,000A, find a value of the temperature T for which the classical and the correct values for the average energy of the mode differ by less than 10%. Problem 3 ( 15 points) In a photoelectric experiment with light of wavelength l the stopping potential is 5V. With light of wavelength 2l the stopping potential is 2V. (a) What is the wavelength l, in A? (b) What is the value of the work function of the metal, in eV? (c) What is the maximum energy of ejected electrons (in eV) for incident light of wavelength 1000A? Justify all your answers to all problems ...
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This note was uploaded on 12/07/2009 for the course PHYS phys 2d taught by Professor Hirsch during the Spring '08 term at UCSD.

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