Modern Physics, 3rd Edition
3rd Edition
ISBN: 9780534493394
Author: Raymond A. Serway, Clement J. Moses, Curt A. Moyer
Publisher: Cengage Learning
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Chapter 7, Problem 3Q
To determine
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Suppose that the electron in the Figure, having a total energy E of 5.1 eV, approaches a barrier of
height Us=6.8 eV and thickness L= 750 pm.
(a) What is the approximate probability that the electron will be transmitted through the barrier, to
appear (and be detectable) on the other side of the barrier?
Energy
Us
Electron
L
Electron of 5 eV is incident on a barrier of height 10 eV and 0.1 nm width.Find the transmission probability of this electron.How will the transmission probability get affected if the width is doubled?
Can a wave packet be formed from a superposition of wave functions of the type ei(kx-ωt) ? Can it be normalized?
Chapter 7 Solutions
Modern Physics, 3rd Edition
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- Consider a potential energy barrier whose height is 6 eV and whose thickness is 0.7 nm. What is the energy (in eV) of an incident electron whose transmission probability is 0.0010? 5.07arrow_forward(a) An electron with initial kinetic energy 32 eV encounters a square barrier with height 41 eV and width 0.25 nm. What is the probability that the electron will tunnel through the barrier? (b) A proton with the same kinetic energy encounters the same barrier. What is the probability that the proton will tunnel through the barrier?arrow_forwardWhen an electron and a proton of the same kinetic energy encounter a barrier of the same height and width, which one of them will tunnel through the barrier more easily? Why?arrow_forward
- Can a quantum particle 'escape' from an infinite potential well like that in a box? Why? Why not?arrow_forwardSuppose a wave function is discontinuous at some point. Can this function represent a quantum state of some physical particle? Why? Why not?arrow_forwardCalculate the transmission probability for quantum-mechanical tunneling in each of the following cases. (a) An electron with an energy deficit of U - E= 0.010 0 eV is incident on a square barrier of width L = 0.100 nm. (b) An electron with an energy deficit of 1.00 eV is incident on the same barrier. (c) An alpha particle (mass 6.64 × 10-27 kg) with an energy deficit of 1.00 MeV is incident on a square barrier of width 1.00 fm. (d) An 8.00-kg bowling ball withan energy deficit of 1.00 J is incident on a square barrier of width 2.00 cm.arrow_forward
- A marble rolls back and forth across a shoebox at a constant speed of 0.8 m/s. Make an order-of-magnitude estimate of the probability of it escaping through the wall of the box by quantum tunneling. State the quantities you take as data and the values you measure or estimate for them.arrow_forwardAccording to the correspondence principle of quantum mechanics, the same results as in classical theory should be obtained when taking very large quantum numbers. Show that when' n o, the probability of finding a particle trapped in a well of infinite potential between x and x + Ax is Ax / L, which is independent of x; this corresponds to the classical probability.arrow_forwardGiven the same particle energy and barrier height and width, which would tunnel more readily: a proton, or an electron? Is your answer consistent with the usual rule of thumb governing when classical or non-classical behavior should prevail?arrow_forward
- Consider an electron of energy 1 eV that encounters a potential barrier of width 0.1nm and energy height 2ev. what is the probability of the electron crossing the barrier? repeat the same calculation for a protonarrow_forwardProblem I mean independent of x as well as 1). In classical mechanics this doesn't change anything, but what about quantum mechanics? Show that the wave function picks up a time-dependent phase factor: exp(-iVot/ħ). What effect does this have on the expectation value of a dynamical variable? Suppose you add a constant Vo to the potential energy (by "constant"arrow_forwardAn electron having total energy E = 4.50 eV approaches a rectangular energy barrier with U = 5.00 eV and L = 950 pm as shown. Classically, the electron cannot pass through the barrier because E < U. Quantum- mechanically, however, the probability of tunneling is not zero. (a) Calculate this probability, which is the transmission coefficient. (b) To what value would the width L of the potential barrier have to be increased for the chance of an incident 4.50-eV electron tunneling through the barrier to be one in one million?arrow_forward
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