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Phys_213_Midterm_2_-_Spring_2007

# Phys_213_Midterm_2_-_Spring_2007 - EXAM II Physics 213...

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Unformatted text preview: EXAM II : Physics 213 Chapters 1,3, and 4 March 7th 2007 The exam contains FOﬂR questions on _S__I_X pages. Except for Question 1, you Mshow all work and give explanations. ****THE CORRECT ANSWER WITH NO EXPLANATIONS OR WORK SHOWN IS WORTH ZERO POINTS. **** Conversely, the WRONG answer with all work shown will be given partial credit IF the steps shown are logical. You may bring ONLY the designated calculator and pencil/pen. Nothing else. All answers reguire units and all vectors require direction. All formulae are on a separate sheet. Good luck! Question 1. /30 points Question 2. /40 points Question 3 /40 points Question 4 /40 points TOTAL /150 Useful constants h: 6.63 X 10‘34 J .s: 4.14 X 10'21 MeV.s c:3 X 108m/s Elementary charge, e=1.6 X 10'19 C Mass of an electron 29.11 X 10‘31 Kg Boltzmann Constant k:1.38 X 10'”J/K=8.62 X 10'5 eV/K Stefan Boltzmann Constant 025.67 X 10'8 W/(m2K4) 8028.85 X 10‘12 F/m 1 eV=l.6 X 10’}9 Joules u0247t X 10‘7 T.m/A Mass of hydrogen atom=1.6727 X 10'27 Kg NAME Q.1. ( 30 pts) 1. ( 10 pts) The ﬁgure shows the Bremsstrahlung spectra of x-rays for electrons incident on tungsten. A 30 keV electron giving up _a_ll_ its kinetic energy would produce x—ray radiation of wavelength [A] < 0.4 A [B] 0.4 A [C] 0.45 A [D] >12 A [E] A range of wavelengths from 0.4 A to > 1.2 A 2. (10 pts)A crystal of potassium bromide has a spacing of 3.3 A. X—rays are incident on it and the ﬁrst order beam emerges at an angle of 17 4" with respect to the incident beam. What is the wavelength of the incident x-rays? [A] 3.3 A past? an. ’3 H v t, t s7”; A . , a 0.5 A 3. ( 10 pts) The work function of platinum is 6.2 eV and that of Zn is 4.24 eV. Electromagnetic radiation of frequency 1.2 X 1015 Hz shines on thin foils of Zn and Pt. The intensity of the light shining on the Pt foil is 3 times that of the light shining on the Zn foil. Which of the following scenarios is correct? Electrons will be emitted from the Pt foil but not the Zn foil. (Elli; lectrons will be emitted from the Zn foil but not the Pt foil. Electrons will be emitted from both foils but the kinetic energy of electrons emitted from the Pt foil will be greater [D] Electrons will be emitted from both but more electrons will be emitted from the Pt foil NAB/IE Q.2. BLACKBODY RADIATION (a) ( 10 pts) Consider a black body at a temperaturesof 10,000K. Calculate the frequency at which the spectral emittance is maximum. M H e’ ‘ W iv “A 5 f "Cisgwwm W)" bl LWMQ ., ,sg 2 ~ » , 5; f 4 1,; A K 3) em: “‘ fr ’ e If s ,,,,,,,,,,, ,. m ‘ wt ., d «M («a H ﬁ> y g. Us». I m)‘ V: :5 q X [05“ Ms / (b) ( 15 pts) An filter is placed between the blackbody of part (a) and a bolometer which measures the total amount of em. power incident. The filter frequency is (5 i 0.0005) X 1014 Hz. Calculate the power registered by the bolometer assuming that the bolometer has an area of 1 m2. The table below ives the emittance at some specific frequencies. Frequency Emittance (watts/m2Hz) i ‘ rs A? .7044X1o-7 A , j I l: to “t lg g, l :2; t x g a) 1/“ My i x EM 4/ mix/(Jigs l/f: I ()0 f X if “WW/5 «l .005; )3: E5355?” M W W} .9 ,l’x wax)”; 51>"l'/?W I w XA‘), lg W t a 6/ W xi‘agf/‘J d‘ W- 5’ g x 5 ﬁg / ” x [f ) H x 52>, “7 (5ny l X/ l (W) {fir‘rrrg/{ei/rm i ﬁx , , _ {l i Ii I E “I f j E y! {A}; 5 j i Elva“ W} / I I‘w/ NAME (c) ( 15 pts) On the axes below , sketch the spectral emittance of the blackbody in (a) radiating at a temperature of 10,000K as a function of frequency. Assume a peak spectral emittance of 6 X 10'7 watt/mZ—Hz. Also on the same sketch, draw the spectral emittance of a blackbody at a temperature T=3333 K. Pay careful attention to the position of the peak and the overall spectrum and indicate these on your sketch. Clearly indicate on your sketch Which curve is which. l '1” ' m gqu’A’Kﬂ/k» i‘ q l WNW ““““““ ””””” """" V 015 ........... Tami: FREQUENCY (H2) y N": '1; MAR/[E Qo3o Consider a Bohr hydrogen atom. The spectral lines are labeled as the Lyman (n21), Balmer (n22), Paschen (n=3), Brackett (n:4) and Pfund (n=5) series where the n value is the final energy state and the frequency of the lines correspond to the energy difference between the initial and final energy states. There are of course other spectral lines corresponding to n>5. The n=1 state is the ground state of the hydrogen atom (a) ( 25 pts) Using the Bohr atom model, what are the initial and f inal energy states for the lowest frequency line in the Lyman series? Give the values of n and E for the initial and final states, calculate the difference in energy and and the frequency of this line in the Lyman series. 5 K . 2V in § , V LW MW?“ Are/Wis i. w I 64m” Mill/«tmisﬁt/gtagitating, i k s it i fix” " 6ft: ,m , 3 f) j) (’37 CW W. A l»; i] \ H“ K “at M ‘06,? Q 77 5;? Alt.) M .i AM)“ it ‘ a WW I’\ y (I; l AAAAA a , j (W towing/)9“ 3} X m, a}, 2 “"‘ ’ arm—t f w gt, 4 EM Will/a 5% >5 it”) I Lifts i» it ls warns n: l Eta—L ’2’ r “l V ,.:§;Wi§j¢primates: Q BEA V (a [ht/Ht Mg) ‘"* A :Mvmﬁzﬂmx [063%,be (b) ( 15 pts) In a hot gas, a particular hydrogen atom is excited into the n=3 state. What is the energy required to remove the electron from this excited hydrogen atom ? it} i mem ‘ £7 mam 7,. F a a m it E v ri 7’“ \ / ﬁll/ﬁgsth NAME (2.4. The Rutherford scattering formula describes the scattering of alpha particles from a thin foil of material and is given by 4am Eb Cat 0/ 2 = 0 ( ) 262 E: kinetic energy of the alpha particle, Z =at0mic number of the foil b: impact parameter. Where (a) ( 15 pts) The diagram below shows an alpha particle of kinetic energy 10 MeV approaching a nucleus. On the diagram, complete the particles trajectory and indicate b and 9. Also consider another alpha particle, with a larger kinetic energy and the same impact parameter. Draw the trajectory of this particle. Carefully indicate which is which. / (b)( 25 pts) A beam of alpha particles of 13:10 MeV is incident upon a gold atom, with atomic number Z: 79. What is the ratio of alpha particle that are deflected by >10o compared to those deﬂected by >60°? (Hint: First calculate the impact parameter) . 0/“ " m?» imaé'itaak .arczfawersjvw S, l?» ,V 4:, w w a; h f U if?{IRAmtg/WW?jam" Ratio: ...
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Phys_213_Midterm_2_-_Spring_2007 - EXAM II Physics 213...

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