Physics 342: Modern Physics

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1 Physics 342: Modern Physics Final Exam (Practice) Relativity: 1) Two LEDs at each end of a meter stick oriented along the x -axis flash simultaneously in their rest frame A. The meter stick is traveling along the +x-axis at a speed β = 0.9 relative to a frame A. What is the time between the flashes in frame A? a) 1 sec b) 7 nsec c) 3 nsec d) 2 sec t = γ t + v x c 2 x = γ x + v t y = y z = z t 1 = 0 " t 2 = γ % $ ' = # c & c = 6.9nsec Hydrogen Atom: 2) How many electron de Broglie wavelengths are there around the circumference in the n = 3 orbit of the Bohr hydrogen atom? a) 1 b) 2 c) 3 d) 6 debroglie Waves: 3) An electron is accelerated through 10 million volts (1x10 7 V). What is it s de Broglie wavelength? a) 1x10-11 m Phys 342 Final Exam

2 b) 1x10-12 m c) 1x10-13 m d) 1x10-14 m pc = K 2 + 2Kmc 2 pc = K 2 + 2Kmc 2 p = e c 10MeV 2 + 2( 10MeV )( 0.51MeV ) = 5.6x10 21 kgm / s λ = h / p =1x10 13 m Schrodinger Equation: 4) For a simple harmonic oscillator with angular frequency ω at T = 0 K, what is the value of <x 2 >? a) x 2 = mω b) x 2 = 2mω c) x 2 = 2 mω d) x 2 = 4 mω 5) An infinite square well has a length L. What is the energy of the n = 2 quantum level? a) 2 2 π 2 ml 2 b) 4 2 π 2 ml 2 c) 2 π 2 2mL 2 d) 2 π 2 ml 2 6) An electron with energy 1 ev is incident on a potential step of height 1.1 ev. What is the decay length δ of the electron wavefunction into the classically-forbidden potential region? a) 12 Å b) 6Å c) 3 nm Phys 342 Final Exam

3 d) 6 nm 2m( E U) k =! ψ exp kx δ =1/ k = 6.2Å = 2m e 0.1eV! = exp( x /δ) =1.6x10 9 m 1 Atomic Physics: 7) What is the electron configuration of 31 Ga? a) 1s 2 2s 2 2p 6 3s 2 3p 6 3d 10 4s 2 4p 1 b) 1s 2 2s 2 3s 2 4s 2 2p 6 3p 6 4p 1 3d 10 c) 1s 2 2s 2 2p 6 3s 2 3p 6 4s 2 3d 10 4p 1 d) 1s 2 2s 2 2p 6 3s 2 3p 6 4s 2 4p 1 3d 10 Thermal Physics: 8) At T = 10,000 K, what is the ratio of the occupancy of the 4S state of hydrogen relative to the 1S state? a) 1.4x10-7 b) 3.8x10-7 c) 7.2x10-6 d) 1.4x10-5 P = exp( ΔE / kt ) = exp(ry( 1/ 4 2 1)e / kt ) = 3.7x10 7 9) What is vrms of an ideal gas? 8k a) B T πm b) c) d) 2k B T m 3k B T m 6k B T πm Phys 342 Final Exam

4 Solid State Physics: 10) Find the Fermi speed, i.e., the speed of a conduction electron whose energy is equal to the Fermi energy E F, for Cu (E F = 7.00 ev) a) 6.9x10 6 m/sec b) 1.0x10 5 m/sec c) 1.0x10 7 m/sec d) 1.6x10 6 m/sec 1 2 mv2 = E F v = 2E F / m e =1.6x10 6 m / s 11) Compute the fractional change in the current through a pn junction diode when the forward bias is changed from V to V. Assume T = 300 K. a) 25% b) 50% c) 100% kbe*t = 25.9 mev d) 200% I = I 0 ( e ev /kt 1) I 1 = I 0 ( e ev1/kt 1) I 2 = I 0 e ev 2 ( /kt 1) =1.47 I 2 = e ev /kt 2 1 I 1 e ev1/kt 1 12) The electron potential well of a metal is -50 ev deep, and the Fermi Energy is +45 ev. A photon with a wavelength of 200 nm is incident on the metal. What is the maximum possible kinetic energy of a photoemmited electron? a) 1.2 ev b) 0.6 ev c) 0.3 ev d) 2.4 ev E = hc λ K = E 5eV =1.2eV Nuclear Physics: Phys 342 Final Exam

5 13) What is the ratio of the amount of U 235 present on Earth today relative to the amount at the birth of Earth 4.5x10 9 years ago: (U 235 half life = 7x10 8 years). a) 10% b) 1% c) 0.1% d) 0.01% N = N 0 2 t/τ 1/2 14) Which nucleus is more stable, 3 H or 3 He? By how many ev? a) 3 H, 19 ev b) 3 He, 19 kev c) 3 H, MeV d) 3 He, MeV (actuall 1.79 MeV) m( 3 H) = m( 3 He) = B He = ( 2m p + 2m e + m n m He )c 2 = MeV B H = ( 2m n + m p + m e m H )c 2 = MeV High-Energy Particle (HEP) Physics: 15) What is a hadron? a) A particle composed of quarks b) A particle composed of leptons c) A particle composed of bosons d) A particle composed of pions 16) Which particle(s) carry the weak nuclear force a) gluon b) photon c) pion d) Z 0, W +, W - AstroPhysics: Phys 342 Final Exam

6 17) An ultramassive black hole resides at the center of our galaxy. It has a mass of 4.5x10 6 suns. The Schwarzshild radius of the Sun is 3 km. What is its Schwarzshild radius of the black hole? a) 3 km b) m c) 10 8 m d) 10 6 km ds 2 = 1 2MG dr 2 c 2 r c 2 dt MG c 2 r + r 2 dω 2 18) What is the diameter of the Milky Way? a) 1 Light Year b) 1000 Light Years c) 10,000 Light Years d) 100,000 Light Years 19) What is the size of the Universe? a) 4.5 Billion Light Years b) 1 Light Year c) Billion Light Years d) 5 Billion Light Years Nonlinear Dynamics and Chaos: 20) What is the stability of the fixed point of the flow: x = x + e y y = y a) saddle b) stable spiral c) unstable spiral d) stable node Phys 342 Final Exam

7 21) What is the Fractal dimension of this dust? Fractal Dust a) 1.00 b) 2.00 c) 1.26 d) 1.46 Dust.ai Phys 342 Final Exam

8 Equations: h = 4.136x10-15 ev sec m e = MeV/c 2 m p = u c = 2.998x10 8 m/s m p = MeV/c 2 m( 1 H) = u e = 1.602x10-19 C m n = u m( 2 H) = u k B = 8.617x10-5 ev/k u = MeV/c 2 m( 3 H) = u hc = 1.24x10 3 ev nm a 0 = Å m( 4 He) = u σ = 5.67x10-8 W/m 2 /K 4 E H = ev G = 6.67x10-11 m 3 /kgs h = 6.63x10-34 Js λ c = 2.426x10-12 m M Sun = 2x10 30 kg m e = 9.1x10-31 kg m p = 1.67x10-27 kg R Sun = 6.95x10 8 m β = u / c γ = 1 v = v' + u 1 β v' u c 2 ν' = ν 1 β 1 + β t = γ t v c x 2 x = γ x vt y = y z = z t = γ t + v x c 2 x = γ x + v t y = y z = z p x = γ p x v c E 2 E = γ E vp x p y = p y p z = p z p x = γ p x + v E c 2 E = γ E + vp x p y = p y p z = p z v x u v x ' = 1 v x u / c 2 v y / γ v y ' = 1 v x u / c 2 v z / γ v z ' = 1 v x u / c 2 E = K + mc 2 p = γ mv E = γ mc 2 E 2 = ( pc) 2 + ( mc 2 ) 2 K = ( γ 1)mc 2 Q = m(x) + m(x) m(y) m(y) c 2 ds 2 = 1 2MG dr 2 c 2 r c 2 dt MG c 2 r S = 1 µ 0 E B νλ = c I = P av A = 1 2µ 0 c E 0 2 2d sinθ = mλ Phys 342 Final Exam

9 E = hν = pc = hc / λ p = h / λ K max = hν φ λ peak T = 2.898x10 3 m K I = σt 4 R(λ) = c 4 8π λ 4 hc / λ e hc / λkt 1 1 E' 1 E = 1 m e c 2 1 cos θ λ c = 2.43 pm pc = K 2 + 2Kmc 2 E = 1 8πε 0 e 2 a 0 n 2 hν = hc λ = K i K f h2 2m 2 ψ + Uψ = Eψ 2 ψ a 0 = 4πε 0 h 2 me 2 r n = a 0 n 2 K = 1 2 U hν max = hc λ min = K i P(r) = r 2 ψ(r) 2 h2 2m 2 ψ ψ + Uψ = ih 2 ψ t ΔE Δt h / 2 Δp Δk h / 2 E n = h2 π 2 n 2 E n = n hω 0 ω 0 = P = ψ 2 k m x n = x n ψ 2 dx k = 2m L 2 2m E U h p = h / λ = hk L = l l + 1 h L z = m l h n( E)dE = g( E) f ( E)dE C V = de m n( v)dv = 4π N 2πk B T f BE ( E) = 1 e α e E /kt 1 3/2 v 2 e mv2 /2k T B 2π N dv n( E)dE = Ee E /kbt de ( πk B T ) 3/2 1 f FD ( E) = e α e E /kt + 1 = 1 ( e E E F )/kt + 1 4π 2m g( E) = 3/2 E I = I h 3 0 ( e ev /kt 1) E g ( 0) = 3.54k B T c Q = ( m x + m X m y m Y )c 2 R = R 0 A 1/3 R 0 =1.2 fm p + uud n udd π + ud π uu + dd R = 2GM c 2 dt Phys 342 Final Exam

10 J = f x g x f y g y λ 1,2 = 1 2 τ ± 1 2 τ 2 4Δ D = ln N 0 ln b outer core electron dynamics (chemistry) inner core electron dynamics nuclear dynamics Vis x-ray γ-ray 10-6 photon electron proton Wavelength (m) atomic radii electron Compton wavelength nuclear radii classical electron radius proton Compton wavelength Kinetic Energy (ev) DeBroglie.grp Phys 342 Final Exam

11 τ Unstable Nodes τ 2-4Δ = 0 Saddle Points 0 Centers Unstable Spirals Stable Spirals Δ non-isolated fixed points Stable Nodes stars & degenerate nodes 0 FxptClass.qpc Phys 342 Final Exam