Unformatted text preview: PHYSICS 2D PROF. HIRSCH Formulas: QUIZ 3 SPRING QUARTER 2005 APRIL 29 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
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† 8p hc / l hc Planck' s law : u( l, T ) = n ( l) ¥ e ( l, T ) = 4 ¥ hc / lkB T ; Wien' s law : lm T = l e -1 4.96 k B 1 Photoelectric effect : eV0 = ( mv 2 ) max = hf - f , f ≡ work function 2 Photons : E = hf = pc ; f = c / l ; Quantum oscillator : en = nhf ; probability P (en ) µ e-e / k T
n B Compton scattering : l' - l = h (1 - cos q ) mec Rutherford scattering : DN = C sin (q / 2)
4 Electrostatics : F = kq1q2 kq (force) ; U = q0 V (potential energy) ; V = (potential) 2 r r 1 1 1 = R( 2 - 2 ) l m n ; R = 1.097 ¥ 10 7 m-1 = 1 911.6 A Hydrogen spectrum :
Bohr atom : E n = - ke 2 Z Z 2E ke 2 mk 2e 4 = - 2 0 ; E0 = = = 13.6eV ; E n = E kin + E pot , E kin = - E pot / 2 = - E n 2 rn n 2 a0 2h2 †
† hf = E i - E f ; rn = r0 n 2 ; r0 = a0 Z ; a0 = h2 = 0.529 A ; L = mvr = nh angular momentum mke 2 † † † † † X - ray spectra : f 1 / 2 = An ( Z - b) ; K : b = 1, L : b = 7.4 Constants : h = 4.136 ¥ 10-15 eV ⋅ s ; hc = 12, 400 eV A ; k B = 1 /11, 600 eV/K ; ke 2 = 14.4 eV A hc = 1973 eV A ; e = 1.6 ¥ 10-19 C ; N A = 6.02 ¥ 10 23 Conversions : 1eV = 1.6 ¥ 10 -19 joules ; 1A = 10 -10 m = 0.1nm ; 1MeV = 10 6 eV Justify all your answers to all problems PHYSICS 2D PROF. HIRSCH Problem 1 (15 points) QUIZ 3 SPRING QUARTER 2005 APRIL 29 2005 In a Rutherford experiment with a particles and target nuclei with atomic number Z=20, the number of particles scattered at angles 90o and 180o is denoted by N9 0 and N1 8 0. With incident a particles of kinetic energy 8MeV it is found N9 0=6480 ; N1 8 0=1620 and with incident a particles of kinetic energy 9MeV it is found N9 0=5140 ; N1 8 0=1028 (a) Explain why these data indicate that the a particles of 8MeV do not penetrate the nucleus and those of 9MeV do. (b) Find upper and lower bounds for the radius of these nuclei from these data. (c) If the incident particles were protons instead of a particles, approximately for what kinetic energy do you expect to find violation of Rutherford's formula for this target? Problem 2 (15 points) Consider a He+ ion (Z=2) with the electron in the n=4 orbit. (a) What are the possible wavelengths of radiation emitted by this ion? Give all the possible values, in A. (b) Give the largest and smallest possible wavelengths of radiation that this ion (with the electron in the n=4 orbit) can absorb, in A. (c) What is the speed of this electron? Give your answer as v/c. Hint: use angular momentum quantization. Problem 3 ( 15 points) Electrons of kinetic energy 59 keV (keV=kilo electron Volt) hit a metal target of atomic number Z=65. (a) What is the minimum wavelength of the emitted X-rays? (b) Estimate the wavelength of the Moseley Ka line for this metal, in A. (c) The emitted X-rays are incident on a crystal and are scattered at an angle of 60o relative to the incident direction. What is the minimum wavelength of the scattered X-rays (in A)? If it is different from the answer in (a), explain the physical reason why it is larger or smaller. 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.
- Spring '08