PHY2D_Quiz6-1

PHY2D_Quiz6-1 - of being anywhere inside this box and zero...

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QUIZ 6 PHYSICS 2D SPRING QUARTER 2009 Professor S.K.Sinha Formulas and constants Mass of electron m e = 9.1. 10 -31 kg Charge on electron = 1.6.10 -19 C Planck’s Constant h= 6.626. 10 -34 J.s =4.136. 10 -15 eV.s h = h / 2 ! = 1.055.10 " 34 J . s = 6.582.10 " 16 eV . s 1 eV =1.6. 10 -19 J Coulomb’s constant k = 1/ (4 !" 0 ) = 8.99.10 9 N . m 2 / kg 2 Velocity of light c = 3.10 8 m/s Energy of photon E = hf For photon λ f = c Compton formula λ′ - λ = (h/m e c)(1 – cos ϕ ) Bragg’s Law n λ =2 d sin θ (n=1,2,……) Bohr’s quantization for Angular momentum mvr = n h Bohr radius a 0 =0.529. 10 -10 m 1 Rydberg (Energy required to ionize hydrogen atom) =13.6 eV Rydberg Constant R = 1.097. 10 7 m -1 Force due to Electric field : F = q E Force due to Magnetic Field: F = q vxB 1. A particle of mass m is bouncing back and forth inside a one- dimensional box between x= -L/2 and x = L/2. It has an equal probability

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Unformatted text preview: of being anywhere inside this box, and zero probability of being outside the box. (a)Calculate the probability distribution of the position of the particle, making sure that the integrated probability is 1. (b) Calculate the standard deviation Δ x of its position, defined as Δ x = [<x 2 > -<x> 2 ] 1/2 where <f(x)> means take the average value of f(x) integrated over the probability distribution. (c)Using Heisenberg’s uncertainty principle, estimate the standard deviation Δ v of its velocity distribution in terms of L and m. (15 points) 2. The phase velocity of a surface wave on a liquid depends on its wavelength via the relation v p = 2 S / "# where S is the surface tension, λ is the wavelength and ρ is the liquid density. Calculate the group velocity of the surface waves in terms of these quantities. (10 pts)...
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PHY2D_Quiz6-1 - of being anywhere inside this box and zero...

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