Under what energy circumstances does an electron tunnel through a potential barrier? A when the potential...
Under what energy circumstances does an electron tunnel through a potential barrier?
|
A |
when the potential energy is greater than the total energy |
|
B |
when the potential energy is less than the total energy |
|
C |
when the kinetic energy is greater than the potential energ |
Homework Answers
tunneling takes place when the when the potential energy is greater than the total energy.
so the correct answer is
(A) when the potential energy is greater than the total energy.
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Under what energy circumstances does an electron tunnel through
a potential barrier?
A
when the potential...
1. Given the potential barrier shown, find the electron energy required for the tunneling probability to...
1. Given the potential barrier shown, find the electron energy required for the tunneling probability to first reach 50%. [V_5eV, a-2nm] Note: The energy may be either less than or greater than the barrier height. You will want to use a graphical solution to find the answer. Plot T as a function of energy and find the lowest energy that crosses 0.5
Consider an electron with energy E in region I confined by a barrier with potential energy...
Consider an electron with energy E in region I confined by a barrier with potential energy Vo and width W. Plot the probability that the electron “tunnels” through the barrier and ends up in Region III as a function of the barrier width for Vo = 1 eV and E = 0.1, 0.25, 0.5, 0.75 and 0.9 eV. Also show the code for the plots.
4. An electron having total energy E 4.50 eV approaches a rectangular Energy energy barrier with...
4. An electron having total energy E 4.50 eV approaches a rectangular Energy energy barrier with U= 5.00 eV and L = 950 pm as shown. Classically, the electron cannot pass through the barrier because E < U. However, quantum mechanically the probability of tunneling is not zero. a) Calculate this probability, which is the transmission coefficient. b) By how much would the width L of the potential barrier have to change for the chance of an incident 4.50-eV electron...
show work thanks. A 10 eV electron (an electron with a kinetic energy of 10 eV)...
show work thanks.
A 10 eV electron (an electron with a kinetic energy of 10 eV) is incident on a potential-energy barrier that has a height equal to 13 eV and a width equal to 1.0 nm. T = e^-2alpha a alpha > > 1 Use the above equation (35-29) to calculate the order of magnitude of the probability that the electron will tunnel through the barrier. 10 _________ Repeat your calculation for a width of 0.10 nm. 10 _________
An electron approaches a 1.9-nm-wide potential-energy barrier of height 7.1 eV. What energy electron has a...
An electron approaches a 1.9-nm-wide potential-energy barrier of height 7.1 eV. What energy electron has a tunneling probability of 10%? What energy electron has a tunneling probability of 1.0%? What energy electron has a tunneling probability of 0.10%?
An electron with a kinetic energy of 47.34 eV is incident on a square barrier with...
An electron with a kinetic energy of 47.34 eV is incident on a square barrier with Ub = 56.43 eV and w = 2.000 nm. What is the probability that the electron tunnels through the barrier? (Use 6.626 ✕ 10−34 J · s for h, 9.109 ✕ 10−31 kg for the mass of an electron, and 1.60 ✕ 10−19 C for the charge of an electron.)
0.91 nm 2.7 nm D | Question 25 4 pts A 2.0 eV electron is incident on a o.20-nm barrier that is 5.67 eV high. What is the probability that this electron will tunnel through the barrier? (1 ev 1.6...
0.91 nm 2.7 nm D | Question 25 4 pts A 2.0 eV electron is incident on a o.20-nm barrier that is 5.67 eV high. What is the probability that this electron will tunnel through the barrier? (1 ev 1.60 10-19 J, m 9.11 10-31 kg. h- 1.055 x 1034 J s, h 6.626 x 1034 j .s) 2.0 x 10-2 1.5 x 10-3 9.0 10-4 1.2 10-3 1.0 x 10-3
0.91 nm 2.7 nm D | Question 25 4...
(III) Quantum Tunneling Consider an electron in 1D in presence of a potential barrier of width...
(III) Quantum Tunneling Consider an electron in 1D in presence of a potential barrier of width L represented by a step function ſo I<0 or 1>L V U. r>0 and 2<L The total wavefunction is subject to the time-independent Schrödinger equation = EV (2) 2m ar2 +V where E is the energy of the quantum particle in question and m is the mass of the quantum particle. A The total wavefunction of a free particle that enters the barrier from...
Under what circumstances is the ERR a more appropriate method than an IRR to evaluate a...
Under what circumstances is the ERR a more appropriate method than an IRR to evaluate a project? A. When the IRR is much greater than the MARR B. When the length of the project is greater than 20 years C. When the IRR is much less than the MARR If the future worth is greater than zero, what does that mean about the project? A. The project will not be profitable B. The project should be considered for funding C....
A free electron moving in the positive x-direction encountering a potential energy barrier in the region...
A free electron moving in the positive x-direction encountering a potential energy barrier in the region x 0 is described by W(x) Aexp(-i2ax/A1) Bexp(-12x/A1) x< 0 (zone I) WI(X) Cexp(i27ox/A) x 20 (zone II) with A 0.80 m-1/2, B 0.20 m-1/2 and C 1.00 m-12. a) Show that the wave function is continaous at x 0. b) Is the electron showing barrier-penetration behavior? Or barrier-transmission behavior? Justify your answer. c) Calculate the probability the electron is reflected at x 0.
1. Given the potential barrier shown, find the electron energy required for the tunneling probability to first reach 50%. [V_5eV, a-2nm] Note: The energy may be either less than or greater than the barrier height. You will want to use a graphical solution to find the answer. Plot T as a function of energy and find the lowest energy that crosses 0.5
4. An electron having total energy E 4.50 eV approaches a rectangular Energy energy barrier with U= 5.00 eV and L = 950 pm as shown. Classically, the electron cannot pass through the barrier because E < U. However, quantum mechanically the probability of tunneling is not zero. a) Calculate this probability, which is the transmission coefficient. b) By how much would the width L of the potential barrier have to change for the chance of an incident 4.50-eV electron...
show work thanks.
A 10 eV electron (an electron with a kinetic energy of 10 eV) is incident on a potential-energy barrier that has a height equal to 13 eV and a width equal to 1.0 nm. T = e^-2alpha a alpha > > 1 Use the above equation (35-29) to calculate the order of magnitude of the probability that the electron will tunnel through the barrier. 10 _________ Repeat your calculation for a width of 0.10 nm. 10 _________
0.91 nm 2.7 nm D | Question 25 4 pts A 2.0 eV electron is incident on a o.20-nm barrier that is 5.67 eV high. What is the probability that this electron will tunnel through the barrier? (1 ev 1.60 10-19 J, m 9.11 10-31 kg. h- 1.055 x 1034 J s, h 6.626 x 1034 j .s) 2.0 x 10-2 1.5 x 10-3 9.0 10-4 1.2 10-3 1.0 x 10-3
0.91 nm 2.7 nm D | Question 25 4...
(III) Quantum Tunneling Consider an electron in 1D in presence of a potential barrier of width L represented by a step function ſo I<0 or 1>L V U. r>0 and 2<L The total wavefunction is subject to the time-independent Schrödinger equation = EV (2) 2m ar2 +V where E is the energy of the quantum particle in question and m is the mass of the quantum particle. A The total wavefunction of a free particle that enters the barrier from...
A free electron moving in the positive x-direction encountering a potential energy barrier in the region x 0 is described by W(x) Aexp(-i2ax/A1) Bexp(-12x/A1) x< 0 (zone I) WI(X) Cexp(i27ox/A) x 20 (zone II) with A 0.80 m-1/2, B 0.20 m-1/2 and C 1.00 m-12. a) Show that the wave function is continaous at x 0. b) Is the electron showing barrier-penetration behavior? Or barrier-transmission behavior? Justify your answer. c) Calculate the probability the electron is reflected at x 0.
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