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Unformatted text preview: Physics 207 Final Exam. Spring 2007
Problem 1 (25 points) Photons with energy 4.70 eV shine on an aluminum surface. The energy required to eject an electron from
the aluminum is 4.20 eV. (3) What is the wavelength of the photons? (5 points) (b) What is the kinetic energy of the fastest electrons that are ejected? (5 points) (c) What is the kinetic energy of the slowest electrons that are ejected? (5 points) (d) What is the stopping potential for this situation? (5 points) (e) What is the longest photon wavelength that can eject electrons from aluminum? (5 points) ox) E4: “‘0 = [1; “'9 )\ z l1Es : iééw’opﬁ)(v’w°6} = ($70,911) ( i .6)! “inf/W) L) Ei :i‘iK +W a Ek I E‘ ‘W: (9,706U—“i.1o€£/) :@
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(a) Photon Wavelength=ﬂ_—F____—W (4) {L\ V:“:.. nhnm nrnilﬂnn‘l :Jnn‘Inll nlWAna— Physics 207 Final Exam, Spring 2007
Problem 2 (25 points) An electron is trapped in a onedimensional inﬁnite potential well that is L=3OU pm wide.
(it) Find the ground state energy and energies of ﬁrst two excited states. (6 points) (b) What is the wavelength of light emitted at electron transition from the second excited to the ﬁrst
excited levels? (3 points) (c) What is the mathematical expression for the wave ﬁmction of an electron in the ﬁrst excited state?
Recall that the normalization factor for all wave function in a onedimensional inﬁnite potential well is A = (/2/L . Why is A important? (4 points) (d) Sketch the probability density (not the wave ﬁinction) for the electron in the ﬁrst excited state. In
which pan(s) xumcly in the well is it most unlikely to detect an electron in the ﬁrst excited state? (6 points) (e) What is the probability that one can detect the electron in the ﬁrst excited state in an interval between
x = 0.5L and x e 0.75L? You should be able to determine this probability by careﬁilly looking at the plot you made in part (d) but you can also calculate the answer, for which the following relation could I: .
be helpﬁJl: Isinz (ta/)4}; = l[ﬂ— Sln 2C? . (6 points)
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Problem 3 (25 points) Consider a square oorr (two dimensional inﬁnite potential well) with widths Lx = Ly =L=20.0 nm.
(a) What is the energy of the lowest energy state for a single electron in the corral? (4 points) ([1) What is the energy of the second lowest energy state for a single electron in the corral? (4 points)
(c) What is the energy of the third lowest energy state for a single electron in the corral? (4 points) (d) What is the energy of the lowest degenerate (more than one state with the same energy) level? How
many different states make up this degenerate level? (4 points) Four electrons are added to the corral. Include electron spin and recall that electrons obey the Pauli
exclusion principle (e) Make a diagram showing which levels the electrons occupy for the lowest energy state of the four
electron system in the corral? What is the energy of this state? (4 points) (I) Make a diagram showing which levels the electrons occupy for the second lowest energy state of the four electron system in the corral? What is the energy of this state? (5 points)
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Short Problem S] (15 points) The equation of a traveling transverse wave is
y z (2.5 mm) sin[(25 m")x + (400 s") z] (a) Calculate the speed and direction in which the wave propagates? (6 points)
(b) Sketch wave at t= 0. (4 points) INA! (“441,6 mm “4. ole Amo‘ W mm L! 91391
(c) Calculate the maximum speed along the y—direction (transverse speed) of particles in the wave. (5 points) ‘ In —)( Alactr», '1 Fl. _._J Physics 207 Final Exam, Spring 2007
Short Problem 32 (15 points) A point source emits sound waves isotropically (equally in all directions) at ﬁ'equency 3 kHz with an average power of 133 W.
(a) What is the wavelength of the sound waves? (3 points) Tﬁ Ihé"§ource‘?"f4~p0i‘rrts§ (c) What is the intensity of sound 1.2 m away ﬂow the source? (4 points) lye sou . (d) What is the sound level in dB 1.2 m away from the source? (4 points) _ (5 M A—
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electric ﬁeld E0? (5 points) (b) After the light passes through P1, what are the intensity I; and electric ﬁeld E}? (5 points) ((1) After the light passes through P2, what are the intensity 12 and electric ﬁeld E2? (5 points) 30° / l/_ _  “' # V/ol
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Short Problem S4 (15 points) A thin lens with focal length f=~10 cm is used to produce an image of an 8 cm tall object that is 15 cm to the leﬁ of the lens as shown in the ﬁgure below. Tick marks in on the optical axis of the ﬁgure indicate 5 cm increments. (a) Draw 2 principal rays in the ﬁgure below to graphically determine the location and appearance
of the resulting image. (6 points) (1)) Calculate the position of the image relative to the lens (how far to left or right of the lens). (5 points) (c) Calculate the height of the image. Is it real or vi n 31. Is it upright or inverted? (4 points) Uta; inqj i CD “40‘ W105" myS v1.4 «(Jenn/V
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Short Problem SS (15 points) The wavelength of yellow light in the glass with index of refraction 1.52 is 388 nm. Find
(a) Speed of the light in glass. (?i points)
. ‘ a (c) Wavelength of the light in air. (3 points)
(d) What is the range of angles (minimum and maximum) with respect to the surface normal for which this light within the glass will be totally internally reﬂected (TIR) when striking the glassair
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Short Problem 86 (15 points) Monochromatic light of wavelength 441 nm is incident on a single narrow slit. On a screen, the distance between the econd diﬁ'ractlo 'nimum and the central maximum is 1.50 m, and the angle of diffraction 6 of the second minimum is 043°.
(:1) What is the distance of the screen ﬁom the slit? (4 points)
(b) What is the width ofthe slit? (4 points) (c) What is the ratio of the intensity at the point 2.0 cm away from the central maximum to the intensity at the central maximum? I (7 points)
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