An electron is in the fourth excited state (count carefully) in a one-dimensional infinite electron trap of width 2.00 nm. What is the shortest wavelength (m) of light that it can emit? The electron mass is 9.10938×10−31 kg. 3.77×10−6 4.21×10−7 9.90×10−6 1.20×10−6 9.32×107 5.50×10−7 6.67×107 1.47×106 2.72×10−6 5.07×106
An electron is in a particular state in a rectangular quantum corral with infinite walls. We probe for it along the dashed lines shown in the figure, which bisect the edges. Along the dashed line parallel to x, the points of maximum probability of detection are separated by Δx = 2.00 pm. Along the dashed line parallel to y, the points of maximum probability are separated by Δy = 3.00 pm. We do not know the edge lengths of the corral or the quantum numbers (symbolize them if you like). What is the energy (J) of the electron? The electron mass is 9.10938×10−31 kg. 1.37×10−14 5.02×10−14 7.33×10−14 2.18×10−14 6.88×10−14 8.13×10−14 5.82×10−14 9.11×10−14 1.80×10−14 6.14×10−14
In Figure (a) below, unpolarized light is sent into a system of three polarizing sheets. The angles θ1, θ2, and θ3 of the polarizing directions are measured counterclockwise from the positive direction of the y axis (they are not drawn to scale). Angles θ1 and θ3 are fixed, but angle θ2 can be varied. Figure (b) gives the intensity of the light emerging from sheet 3 as a function of θ2. (The scale of the intensity axis is not indicated. ) What percentage of the light's initial intensity is transmitted by the system when θ2 = 64∘? Number Units
Figure (a) below shows a lens with radius of curvature R = 5.9 m and the diameter D = 22 mm lying on a flat glass plate and illuminated from above by light with wavelength λ = 628 nm. Figure (b) below (a photograph taken from above the lens) shows that circular interference fringes (called Newton's rings) appear, associated with the variable thickness d of the air film between the lens and the plate. In this Newton's rings experiment (a) how many bright rings are produced? (b) How many bright rings would be produced if the arrangement were immersed in water (n = 1.33)? (a) (b) (a) Number Units (b) Number Units
In the figure, a long rectangular conducting loop, of width L = 13 cm, resistance R = 12 Ω, and mass m = 0.082 kg , is hung in a horizontal, uniform magnetic field of magnitude 1.1 T that is directed into the page and that exists only above line aa. The loop is then dropped; during its fall, it accelerates until it reaches a certain terminal speed vt. Ignoring air drag, find the terminal speed. Number Units
As a loop of wire with a resistance of 10 Ω moves in a constant non-uniform magnetic field, it loses kinetic energy at a uniform rate of 5.0 mJ/s. The induced current in the loop is: 0 A 2.0 mA 2.8 mA 22 mA cannot be calculated from the given data
In an oscillating LC circuit, L = 3.82 mH and C = 3.85 μF. At t = 0 the charge on the capacitor is zero and the current is 2.63 A. (a) What is the maximum charge that will appear on the capacitor? (b) At what earliest time t > 0 is the rate at which energy is stored in the capacitor greatest, and (c) what is that greatest rate? (a) Number Units (b) Number Units (c) Number Units
In an oscillating LC circuit, the total stored energy is U and the maximum charge on the capacitor is Q. When the charge on the capacitor is Q/2, the energy stored in the inductor is: 3U/2 (4/3)U U/2 U/4 3U/4
In the figure an electric field is directed out of the page within a circular region of radius R = 3.50 cm. The magnitude of the electric field is given by E = (0.800 V/m⋅s)(1 − r/R)t, where radial distance r ≤ R and t is in seconds. What is the magnitude of the magnetic field that is induced at radial distances (a) 2.50 cm and (b) 5.50 cm? (a) Number Units (b) Number Units
A 1.2-m radius cylindrical region contains a uniform electric field along the cylinder axis. It is increasing uniformly with time. To obtain a total displacement current of 2.0×10−9 A through a cross section of the region, the magnitude of the electric field should change at a rate of: 5.0 V/m. s 12 V/m⋅s 37 V/m⋅s 50 V/m⋅s 4.0×107 V/m⋅s
In Figure (a) below, unpolarized light is sent into a system of three polarizing sheets. The angles θ1, θ2, and θ3 of the polarizing directions are measured counterclockwise from the positive direction of the y axis (they are not drawn to scale). Angles θ1 and θ3 are fixed, but angle θ2 can be varied. Figure (b) gives the intensity of the light emerging from sheet 3 as a function of θ2. (The scale of the intensity axis is not indicated. ) What percentage of the light's initial intensity is transmitted by the three-sheet system when θ2 = 90∘? (a) (b)
Light with an intensity of 1 kW/m2 falls normally on a surface and is completely reflected. The radiation pressure is: 1 kPa 3×1011 Pa 1.7×10−6 Pa 3.3×10−6 Pa 6.7×10−6 Pa
Spherical mirrors. Object O stands on the central axis of a spherical mirror. For this situation object distance is ps = +26 cm, the type of mirror is concave, and then the distance between the focal point and the mirror is 38 cm (without proper sign). Find (a) the radius of curvature r (including sign), (b) the image distance i, and (c) the lateral magnification m. Also, determine whether the image is (d) real or virtual, (e) inverted from object O or noninverted, and (f) on the same side of the mirror as O or on the opposite side. (a) Number Units (b) Number Units (c) Number Units (d) (e)
The image of an erect candle, formed using a convex mirror, is always: virtual, inverted, and smaller than the candle virtual, inverted, and larger than the candle virtual, erect, and larger than the candle virtual, erect, and smaller than the candle real, erect, and smaller than the candle
Figure (a) below shows a lens with radius of curvature R = 256 mm lying on a flat glass plate and illuminated from above by light with wavelength λ = 560 nm. Figure (b) below (a photograph taken from above the lens) shows that circular interference fringes (called Newton's rings) appear, associated with the variable thickness d of the air film between the lens and the plate. (a) Find the difference in radius between adjacent bright rings (maxima) Δr = r57 − r56 and (b) the area between this adjacent bright rings. Assume that λ/R < < 1. (a) (b)
In a Young's double-slit experiment, the slit separation is doubled. To maintain the same fringe spacing on the screen, the screen-to-slit distance D must be changed to: D/2 D/2 D2 2D 4D
A diffraction grating having 190 lines/mm is illuminated with a light signal containing only two wavelengths, λ1 = 428 nm and λ2 = 535 nm. The signal is incident perpendicularly on the grating. (a) What is the angular separation between the second-order maxima of these two wavelengths? (b) What is the smallest angle at which two of the resulting maxima are superimposed? (c) What is the highest order for which maxima for both wavelengths are present in the diffraction pattern? (a) Number Units (b) Number Units (c) Number Units
At the first minimum adjacent to the central maximum of a single-slit diffraction pattern the phase difference between the Huygens wavelet from the top of the slit and the wavelet from the midpoint of the slit is: π/8 rad π/4 rad π/2 rad πrad 3π/2 rad
A certain particle of mass m has momentum of magnitude mc. What are (a) β, (b) γ, and (c) the ratio K/E0? (a) Number Units (b) Number Units (c) Number Units
Particle A (with rest energy 216 MeV) is at rest in a lab frame when it decays to particle B (rest energy 108 MeV) and particle C (rest energy 54 MeV). What are the (a) total energy and (b) momentum of B and the (c) total energy and (d) momentum of C ? (a) Number Units (b) Number Units (c) Number Units (d) Number Units
Two flashes of light occur simultaneously at t = 0 in reference frame S, one at x = 0 and the other at x = 600 m. They are observed in reference frame S′, which is moving at 0.95 c in the positive x direction. The origins of the two frames coincide at t = 0 and the clocks of S are zeroed when the origins coincide. In S' the coordinate where the leading edges of the two light flashes meet and the time when they meet are: 48 m, 0.16 μs 15 m, 0.050 μs 300 m, 1.0 μs 585 m, 1.95 μs 1900 m, 0.16 μs
Two events occur 100 m apart with an intervening time interval of 0.60 μs. The speed of a reference frame in which they occur at the same coordinate is: 0 c 0.25c 0.56c 1.1c 1.8c
Calculate the Compton wavelength for (a) an electron and (b) a proton. What is the photon energy for an electromagnetic wave with a wavelength equal to the Compton wavelength of (c) the electron and (d) the proton? (a) Number Units (b) Number Units (c) Number Units (d) Number Units
A free electron and a free proton have the same momentum. This means that, compared to the matter wave associated with the proton, the matter wave associated with the electron has: a shorter wavelength and a greater frequency a longer wavelength and a greater frequency the same wavelength and the same frequency the same wavelength and a greater frequency the same wavelength and a smaller frequency
If an electron has a de Broglie wavelength of 2.40 pm (that is, 2.40×10−12 m), what is its kinetic energy (J)? This is a relativistic situation. Electron rest energy = 0.511 MeV. 7.33×10−15 5.21×10−12 1.90×10−11 2.46×10−13 9.60×10−11 3.46×10−14 1.03×10−13 4.94×10−13 6.77×10−13 5.77×10−12
In the ground state of the hydrogen atom, the electron has a total energy of -13.6 eV . What are (a) its kinetic energy and (b) its potential energy if the electron is a distance 4.0 a from the central nucleus? Here a is the Bohr radius. (a) Number Units (b) Number Units
A hydrogen atom, initially at rest in the n = 5 quantum state, undergoes a transition to the ground state, emitting a photon in the process. What is the speed of the recoiling hydrogen atom? Number Units
A proton is in a particular state in a rectangular quantum corral with infinite walls. We probe for it along the dashed lines shown in the figure. Along the dashed line that bisects the edge length along y and that is parallel to x, the points of maximum probability of detection are separated by Δx = 5.00 pm. Along the dashed line that bisects the edge length along x and that is parallel to y, the points of maximum probability are separated by Δy = 8.00 pm. We do not know the edge lengths of the corral or the quantum numbers (symbolize them if you like). What is the energy (J) of the proton? The proton mass is 1.673×10−27 kg. 1.37×10−17 2.18×10−18 1.83×10−18 7.33×10−17 5.02×10−18 9.11×10−17 6.14×10−17 8.13×10−18 6.88×10−18 5.82×10−17
An electron is in the fourth excited state (count carefully) in a one-dimensional infinite electron trap of width 2.00 nm. What is the longest wavelength (m) of light that it can absorb? The electron mass is 9.10938×10−31 kg. 5.50×10−7 9.90×10−6 6.67×10−7 3.77×10−6 9.32×10−7 1.47×10−6 1.20×10−6 5.07×10−6 4.21×10−7 2.72×10−6
In the figure, a uniform sphere of mass m = 1.07 kg and radius r = 0.261 m is held in place by a massless rope attached to a frictionless wall a distance L = 1.60 m above the center of the sphere. Find (a) the tension in the rope and (b) the force on the sphere from the wall. (a) Number Units (b) Number Units
A 120 g ball with speed 4.3 m/s strikes a wall perpendicularly and rebounds in the opposite direction with the same speed. The collision lasts 4.0 ms. What are the magnitudes of the (a) impulse and (a) average force on the wall from the ball? (a) Number Units (b) Number Units
A 0.31−kg particle has a speed of 5.0 m/s at point A and kinetic energy of 8.2 J at point B. (a) What is its kinetic energy at A? J (b) What is its speed at point B? m/s (c) What is the total work done on the particle as it moves from A to B? J
A 705 N bear is standing on a metal plank supported by the cable shown in the figure. At the end of the plank hangs a basket weighing 80 N. Assume the plank is uniform, weighs 200 N, is 5.00 m long, and θ = 60.0∘. (a) When the bear is at x = 1.15 m, find the tension in the cable supporting the plank and the components of the force exerted by the wall on the left end of the plank. (Enter the magnitudes of your answers in N.) T = N Fx = N Fy = N (b) If the cable can withstand a maximum tension of 800 N , what is the maximum distance (in m ) the bear can walk before the cable breaks? (Measure this distance from the wall.) m
A horizontal wire is hung from the ceiling of a room by two massless strings. The wire has a length of 0.20 m and a mass of 0.080 kg. A uniform magnetic field of magnitude 0.070 T is directed from the ceiling to the floor. When a current of l = 42 A exists in the wire, the wire swings upward and, at equilibrium, makes an angle φ with respect to the vertical, as the drawing shows. (a) Draw the free-body diagram showing the forces that act on the wire. Account for each of the strings separately. (b) Find the angle φ. (c) Find the tension in each of the two strings.