Physics for Scientists & Engineers, Volume 2 (Chapters 21-35)
5th Edition
ISBN: 9780134378046
Author: GIANCOLI, Douglas
Publisher: PEARSON
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Chapter 38, Problem 21P
To determine
The proof that uncertainty principle holds for a “wave packet” formed by two similar waves; width of each wave packet is
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(b) (deBroglie wave length) Determine the deBroglie wavelength (formula: p=h/2) of a
grain of dust with diameter 1um, density 1kg m-3 and speed 1cm s. Compare your
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(a) Show that the spread of velocities caused by the uncertainty principle does not have measurable consequences for macroscopic objects (objects that are large compared with atoms) by considering a 100-g racquetball confined to a room 15 m on a side. Assume the ball is moving at 2.0 m/s along the x axis.
(10) i) Use the quantum mechanical kinetic energy operator T, =
to find the kinetic energy of the first
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Chapter 38 Solutions
Physics for Scientists & Engineers, Volume 2 (Chapters 21-35)
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- (a) Calculate the minimum uncertainty in momentum (expressed in MeV/?) for a proton confined to a nucleus of diameter 5.0 fm. (1 fm = 1 * 10-15 m). (b) A proton (rest mass 938.3 MeV/?2) in a nucleus of radius 6.0 fm has a kinetic energy of 5.6 MeV. If the proton were represented by a de Broglie wave, how many wavelengths could fit across the diameter of that nucleus? (1 fm = 1 * 10-15 m). (c) Electrons (rest mass 0.51 MeV/?2) moving with a speed of 1.60 × 105 m/s are described by a wave packet of width 2.65 nm. What range of values will most likely result from a measurement of the speed of the electrons? Please use:ℎ? 1240 eVnmℏ? 197 eVnmarrow_forward(b) Sketch and write the mathematical expression of the wavefunction of an electron occupying the level n 6 in a 1ID infinite quantum well of width 3.5x10" m. (c) A radio station broadcasts on a frequency of 200 kHz by using a 200 kW transmitter. () Estimate the number of photons striking a 1 square metre acrial each second at a distance of 1000 km. (ii) What is the energy () and momentum (kg m/s) of the photons? (ii) What is the number of photons emitted in 2 second by the transmitter?arrow_forward(i) Compare stimulated and spontaneous emission. What is the significance of Einstein's coefficients? (ii) Calculate the frequency difference between resonant longitudinal 20th mode and 21th mode, if the cavity length is 20 cm.arrow_forward
- (b) An electron confined in a one dimensional box emits a 200 nm photon in a quantum jump from n = 2 to n = 1. What is the length of the box? The mass of an electron is 9.11 x 1031 kg. (c) A proton confined in a one dimensional box emits a 2.0 MeV gamma-ray photon in a quantum jump from n = 2 to n = 1. What is the length of the box? The mass of a proton is 1.67 x 1027 kg.arrow_forward(i) Show that the classical Rayleigh-Jeans formula is a special case of Planck's radiation formula. (ii) Given a wave function of a particle as = Ae-ip/hy, confined such that 0arrow_forwardAn electron and a proton, each initially at rest, are accelerated across the same voltage. Assuming that the uncertaintyin their position is given by their de Broglie wavelength,find the ratio of the uncertainty in their momentum.arrow_forwardThis question is for modern physics and wave and particle: (a) To how small a region must an electron be confined for borderline relativistic speeds – say, 0.05c – to become reasonably likely? (Ans: 3.9×10^−12m ) (b) On the basis of this, would you expect relativistic effects to be prominent for hydrogen’s electron, which has an orbit radius near 10-10? For a lead atom “inner-shell” electron of orbit radius 10-12m?arrow_forward(c) Below is the expression of quantized subband energy in a quantum well photodetector where the m* and Wz are the carrier effective mass and well width, respectively, and the rest are constants. Derive the wavelength detected based on intersubband transition. En = ħ2 nn *W. 2m Zarrow_forwardUse the uncertainty principle to show that if an electron were confined inside an atomic nucleus of diameter 2 x 10-15 m, it would have to be moving relativistically, whereas a proton confined to the same nucleus can be moving nonrelativistically.arrow_forward(i) Is an electron a particle? Is it a wave? Explain your answer citing relevant experimental evidence. Calculate the De-Broglie wavelength of an electron having a kinetic energy of 1000eV. Compare the result with wavelength of X-rays having the same energy.arrow_forwardConsider an electron with a (non-relativistic) kinetic energy of 1 eV. (i) What is the electron speed in m/s? What is the de Broglie wavelength of the electron? (ii) Consider a beam of 1 eV electrons incident on a pair of very thin slits, separated by a distance d, with an interference pattern seen on a screen 2 m beyond the slits. Find the value of d such that the position of the first off-center bright fringe of the pattern is located 0.5mm from the center of the pattern.arrow_forward(i) Calculate the zero point energy of a harmonic oscillator consisting of a particle of mass 2.5 × 10−26 kg witha force constant 125 N m−1. Calculate the wavelength of a photon needed to excite a transition between the neighbouring energy levels of this harmonic oscillator. (ii) Calculate the zero point energy of a harmonic oscillator consisting of a particle of mass 2.0 × 10−26 kgwith a force constant 120 N m−1.arrow_forwardarrow_back_iosSEE MORE QUESTIONSarrow_forward_ios
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