Physics for Scientists and Engineers with Modern, Revised Hybrid (with Enhanced WebAssign Printed Access Card for Physics, Multi-Term Courses)
9th Edition
ISBN: 9781305266292
Author: Raymond A. Serway, John W. Jewett
Publisher: Cengage Learning
expand_more
expand_more
format_list_bulleted
Question
Chapter 41, Problem 47AP
(a)
To determine
Transmission probability for
(b)
To determine
Transmission probability for quantum mechanical tunnelling of electron with energy deficit of
(c)
To determine
Transmission probability for quantum mechanical tunnelling of alpha particle with energy deficit of
(d)
To determine
Transmission probability for quantum mechanical tunnelling of a bowling ball with energy deficit of
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
Quantum mechanical tunnelling enables chemical reactions to proceed that would be
energetically impossible in classical mechanics. Assume that hydrogen (H) and tritium
(T) atoms, each with a kinetic energy of 0.9 eV, encounter a potential barrier that is 1.0
eV high and 100 pm broad. Calculate the ratio of probabilities for transmission of the H
and T atoms through the barrier.
Note: the masses of H and T atoms are 1.674 x 10-27 kg and 5.008 x 10-27 kg, respectively,
and 1 eV=1.602x10-19 J.
Calculate 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.
In a simple model for a radioactive nucleus, an alpha particle (m = 6.64 * 10-27 kg) is trapped by a square barrier that has width 2.0 fm and height 30.0 MeV.
(a) What is the tunneling probability when the alpha particle encounters the barrier if its kinetic energy is 1.0 MeV below the top of the barrier (Fig. )?
(b) What is the tunneling probability if the energy of the alpha particle is 10.0 MeV below the top of the barrier?
Chapter 41 Solutions
Physics for Scientists and Engineers with Modern, Revised Hybrid (with Enhanced WebAssign Printed Access Card for Physics, Multi-Term Courses)
Ch. 41.1 - Prob. 41.1QQCh. 41.2 - Prob. 41.2QQCh. 41.2 - Prob. 41.3QQCh. 41.5 - Prob. 41.4QQCh. 41 - Prob. 1OQCh. 41 - Prob. 2OQCh. 41 - Prob. 3OQCh. 41 - Prob. 4OQCh. 41 - Prob. 5OQCh. 41 - Prob. 6OQ
Ch. 41 - Prob. 7OQCh. 41 - Prob. 8OQCh. 41 - Prob. 9OQCh. 41 - Prob. 10OQCh. 41 - Prob. 1CQCh. 41 - Prob. 2CQCh. 41 - Prob. 3CQCh. 41 - Prob. 4CQCh. 41 - Prob. 5CQCh. 41 - Prob. 6CQCh. 41 - Prob. 7CQCh. 41 - Prob. 8CQCh. 41 - Prob. 1PCh. 41 - Prob. 2PCh. 41 - Prob. 3PCh. 41 - Prob. 4PCh. 41 - Prob. 5PCh. 41 - Prob. 6PCh. 41 - Prob. 7PCh. 41 - Prob. 8PCh. 41 - Prob. 9PCh. 41 - Prob. 10PCh. 41 - Prob. 11PCh. 41 - Prob. 12PCh. 41 - Prob. 13PCh. 41 - Prob. 15PCh. 41 - Prob. 16PCh. 41 - Prob. 17PCh. 41 - Prob. 18PCh. 41 - Prob. 19PCh. 41 - Prob. 20PCh. 41 - Prob. 21PCh. 41 - Prob. 22PCh. 41 - Prob. 23PCh. 41 - Prob. 24PCh. 41 - Prob. 25PCh. 41 - Prob. 26PCh. 41 - Prob. 27PCh. 41 - Prob. 28PCh. 41 - Prob. 29PCh. 41 - Prob. 30PCh. 41 - Prob. 31PCh. 41 - Prob. 32PCh. 41 - Prob. 33PCh. 41 - Prob. 34PCh. 41 - Prob. 36PCh. 41 - Prob. 37PCh. 41 - Prob. 38PCh. 41 - Prob. 39PCh. 41 - Two particles with masses m1 and m2 are joined by...Ch. 41 - Prob. 41PCh. 41 - Prob. 42PCh. 41 - Prob. 43APCh. 41 - Prob. 44APCh. 41 - Prob. 45APCh. 41 - Prob. 46APCh. 41 - Prob. 47APCh. 41 - Prob. 48APCh. 41 - Prob. 49APCh. 41 - Prob. 50APCh. 41 - Prob. 51APCh. 41 - Prob. 52APCh. 41 - Prob. 53APCh. 41 - Prob. 54APCh. 41 - Prob. 56APCh. 41 - Prob. 57APCh. 41 - Prob. 58APCh. 41 - Prob. 59CPCh. 41 - Prob. 60CPCh. 41 - Prob. 61CPCh. 41 - Prob. 62CPCh. 41 - Prob. 63CP
Knowledge Booster
Similar questions
- If STM is to detect surface features with local heights of about 0.0200 nm, what percent change in tunneling-electron current must the STM electronics be able to detect? Assume that the tunneling-electron current has characteristics given in the preceding problem.arrow_forwardThe energy of a proton is 1.0 MeV below the top of a 6.8-fm-wide energy barrier. What is the probability that the proton will tunnel through the barrier? (1 eV = 1.60 × 10-19 J, mproton = 1.67 × 10-27 kg, ħ = 1.055 × 10-34 J ∙ s, h = 6.626 × 10-34 J ∙ s)arrow_forwardTwo copper nanowires are insulated by a copper oxide nano-layer that provides a 10.0-eV potential barrier. Estimate the tunneling probability between the nanowires by 7.00-eV electrons through a 5.00-nm thick oxide layer. What if the thickness of the layer were reduced to just 1.00 nm? (Hint: the rest mass of the electron (m) = 511 keV/c2, ℏ = 0.1973 keVnm/c)arrow_forward
- A stream of electrons, each with a kinetic energy of 450 eV, is sent through a potential-free region toward a potential barrier of "height" 500 eV and thickness 0.300 nm. The stream consists of 1 × 1015 electrons. How many should tunnel through the barrier? Pick the closest answer. The electron mass is 9.10938 x 10-31 kg. O 8 x 107 O 8 × 10⁹ 3 x 10³ 6 x 104 4x 107 4 x 105 O 1 x 106 O 7 x 104 Ⓒ 9 × 105 O 7 x 106arrow_forwardA beam of electrons is incident on a barrier that is 0.60 nm wide and 6.40 eV high. If the number of electrons striking the barrier each second is 6.50 ✕ 1021 /s with an energy of 5.35 eV, then how long would it take for a single electron to be transmitted through the barrier?arrow_forwardAn electron with kinetic energy E = 5.50 eV is incident on a barrier of width L = 0.190 nm and height U = 10.0 eV. Energy 0 (a) What is the probability that the electron tunnels through the barrier? (Use 9.11 × 10-31 kg for the mass of an electron, 1.055 × 10¯³4 J · s for h, and note that there are 1.60 × 10¯ % (b) What is the probability that the electron is reflected? % What If? For what value of U (in eV) would the probability of transmission be exactly 25.0% and 50.0%? (c) 25.0% (d) 50.0% eV eV -19 J per eV.)arrow_forward
- An electron with a kinetic energy of 44.34 eV is incident on a square barrier with Up = 57.43 eV and w = 2.200 nm. What is the probability that the electron tunnels through the barrier? (Use 6.626 x 1034 j x S for h, 9.109 x 1031 kg for the mass of an electron, and 1.60 x 1019 C for the charge of an electron.)arrow_forwardA single electron of mass m can move freely along a one-dimensionl gold nanowire. Let x be the position coordinate of the electron along the wire. (a) Let ø (x) be the wave function of the electron. The quantity |ø (x)| has dimensions of inverse length. Explain very briefly the meaning of this quantity as a probability density. (b) Let us assume that $ (x) = A sin (3kox) (2) where A and ko are fixed, positive constants. Establish whether this wave function represents an eigenstate of momentum p. Justify your answer. Hint: the momentum operator is p -ih. - (c) Establish whether the wave function (x) given in Eq. (2) represents an eigenstate of kinetic energy K. Justify your answer. Hint: the kinetic energy operator is K = p²/2m. (d) Let us now assume that the gold nanowire mentioned above is not infinite, but extends over a finite length from r= 0 to x = L. Inside this region, the potential energy of the electron is zero, but outside this region the potential energy is infinite…arrow_forward= = An electron having total energy E 4.60 eV approaches a rectangular energy barrier with U■5.10 eV and L-950 pm as shown in the figure below. Classically, the electron cannot pass through the barrier because E < U. Quantum-mechanically, however, the probability of tunneling is not zero. Energy E U 0 i (a) Calculate this probability, which is the transmission coefficient. (Use 9.11 x 10-31 kg for the mass of an electron, 1.055 x 10-34] s for h, and note that there are 1.60 x 10-19 J per eV.) (b) To what value would the width L of the potential barrier have to be increased for the chance of an incident 4.60-eV electron tunneling through the barrier to be one in one million? nmarrow_forward
- Consider a three-level quantum system with a given energy levels E₁ = 0, E₂ = 1.0 x 10-23 J with a degeneracy of three and E3 = 3.10 x 10-23 J. Determine the probabilities for each energy levels if the heat bath has a temperature of 5 K.arrow_forwardA certain atom remains in an excited state for about 51.7 ns before emitting a 2.15-eV photon and transitioning to the ground state. What is the uncertainty in the frequency of the photon in Hz?arrow_forwardA quantum mechanical particle moving in one dimension between impenetrable barriers has energy levels ϵ,4ϵ,9ϵ,...ϵ, 4ϵ, 9ϵ, ... , that is En=ϵn2En=ϵ n2 . Suppose that ϵ=0.035eVϵ =0.035 eV for a certain such quantum system. What is the probability (as a percent) that such a system will be in its ground state when it is in contact with a reservoir at room temperature? The probability that the system will be in its ground state when it is in contact with a reservoir at room temperature isarrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
Principles of Physics: A Calculus-Based TextPhysicsISBN:9781133104261Author:Raymond A. Serway, John W. JewettPublisher:Cengage Learning
University Physics Volume 3PhysicsISBN:9781938168185Author:William Moebs, Jeff SannyPublisher:OpenStax
Principles of Physics: A Calculus-Based Text
Physics
ISBN:9781133104261
Author:Raymond A. Serway, John W. Jewett
Publisher:Cengage Learning
University Physics Volume 3
Physics
ISBN:9781938168185
Author:William Moebs, Jeff Sanny
Publisher:OpenStax