Physics for Scientists and Engineers
6th Edition
ISBN: 9781429281843
Author: Tipler
Publisher: MAC HIGHER
expand_more
expand_more
format_list_bulleted
Question
Chapter 35, Problem 9P
(a)
To determine
The value of
(b)
To determine
The lowest energy for the electron.
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solutionStudents have asked these similar questions
An electron with kinetic energy E = 3.10 eV is incident on a barrier of width L = 0.230 nm and height U = 10.0 eV
(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 ℏ, and note that there are 1.60 ✕ 10−19 J per eV.)
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%
(a) What is the separation in energy between the lowest two energy levels for a container 20 cm on a side containing argon atoms? Assume, for simplicity, that the argon atoms are trapped in a one-dimensional well 20 cm wide. The molar mass of argon is 39.9 g/mol. (b) At 300 K, to the nearest power of ten, what is the ratio of the thermal energy of the atoms to this energy separation? (c) At what temperature does the thermal energy equal the energy separation?
(a) Calculate the energy separations in units of joules and kilojoules per mole, respectively, between thelevels n = 2 and n = 1 of an electron in a one-dimensional box of length 1.0 nm.
(b) Calculate the zero point energy of a harmonic oscillator consisting of a particle of mass 2.33 × 10−26 kgwith a force constant 155 N m−1.
Chapter 35 Solutions
Physics for Scientists and Engineers
Ch. 35 - Prob. 1PCh. 35 - Prob. 2PCh. 35 - Prob. 3PCh. 35 - Prob. 4PCh. 35 - Prob. 5PCh. 35 - Prob. 6PCh. 35 - Prob. 7PCh. 35 - Prob. 8PCh. 35 - Prob. 9PCh. 35 - Prob. 10P
Ch. 35 - Prob. 11PCh. 35 - Prob. 12PCh. 35 - Prob. 13PCh. 35 - Prob. 14PCh. 35 - Prob. 15PCh. 35 - Prob. 16PCh. 35 - Prob. 17PCh. 35 - Prob. 18PCh. 35 - Prob. 19PCh. 35 - Prob. 20PCh. 35 - Prob. 21PCh. 35 - Prob. 22PCh. 35 - Prob. 23PCh. 35 - Prob. 24PCh. 35 - Prob. 25PCh. 35 - Prob. 26PCh. 35 - Prob. 27PCh. 35 - Prob. 28PCh. 35 - Prob. 29PCh. 35 - Prob. 30PCh. 35 - Prob. 31PCh. 35 - Prob. 32PCh. 35 - Prob. 33PCh. 35 - Prob. 34PCh. 35 - Prob. 35PCh. 35 - Prob. 36PCh. 35 - Prob. 37PCh. 35 - Prob. 38P
Knowledge Booster
Similar questions
- The radial function of a particle in a central potential is give by wave [ - r R(r) = A-exp where A is the normalization constant and a is positive constant еxp а 2a of suitable dimensions. If ya is the most probable distance of the particle from the force center, the value of y isarrow_forwardLet V = 2xyz3 +3 In(x² + 2y² + 3z²) V in free space. Evaluate each of the following quantities at P(3, 2, –1): (a) V; (b) |V|; (c) E; (d) |E|; (e) a (f) D.arrow_forwardLet's consider a harmonic oscillator. The total energy of this oscillator is given by E=(p²/2m) +(½)kx?. A) For constant energy E, graph the energies in the range E to E + dE, the allowed region in the classical phase space (p-x plane) of the oscillator. B) For k = 6.0 N / m, m = 3.0 kg and the maximum amplitude of the oscillator xmax =2.3 m For the region with energies equal to or less than E, the oscillator number of states that can be entered D(E).arrow_forward
- Consider a potential barrier defined by = U (x) T = with Uo 1.00 eV. An electron with energy E > 1 eV moving in the positive x- direction is incident on this potential. The transmission probability for this situation is given by x L 4(E/Uo) [(E/Uo) - 1] sin² [√2m(E – U₁)L/ħ] + 4(E/U₁) [(E/U₁) − 1] It is found that the reflection probability is zero for E = 1.10 eV and non-zero for smaller incident energies. What is the width of the potential barrier L?arrow_forwardone-dimensional A one-particle, system has the potential energy function V = V₁ for 0 ≤ x ≤ 1 and V = ∞ elsewhere (where Vo is a constant). a) Use the variation function = sin() for 0 ≤ x ≤ 1 and = 0 elsewhere to estimate the ground-state energy of this system. b) Calculate the % relative error.arrow_forwardProblem 3: Chemical potential of an Einstein solid. Consider an Einstein solid for which both N and q are much greater than 1. Think of each ocillator as a separate “particle". a) Show that the chemical potential is H = -kT In (**e) b) Discuss this result in the limits N » q and N « q, concentrating on the question of how much S increases when another particle carrying no energy is added to the system. Does the formula make intuitive sense?arrow_forward
- According to the equipartition theorem of classical thermodynamics, all ocillators in the cavity have the same mean energy, irrespective of their frequencies. With this in view, prove the following relation: 00 EE¬E/kT dE = = kT . S" e-E/KT dEarrow_forwardConsider a 1-dimensional quantum system of one particle Question 01: in which the particle is under a potential V(x) = mw?a?, with m being the mass of the particle and w being a parameter (you may take it as angular fre- quency) with inverse dimension of time. The particle may be found in the region -0 < x < o. Varify that the lowest two states of the system are mutually orthonormal.arrow_forwardA quantum system is composed of an electron in free movement in a region one- dimensional, between O and L = 1.00 x 10-10 m. Now consider that the system is subject to a potential given by V(x) = -e sin(ax/L), where ɛ = 6.00 x 10-28 J. With Based on First Order Perturbation Theory, calculate the energy of the state fundamental of the system and compare with the value obtained in the absence of the potential.arrow_forward
- (a) Derive an expression for the variance in the number of particles in a state for a Bose- Einstein gas when the number of particles in the gas can change. (b) Using the particle number for the Bose-Einstein gas, determine any specific properties of the chemical potential.arrow_forwardWe can approximate an electron moving in a nanowire (a small, thin wire) as a one-dimensional infi nite square-well potential. Let the wire be 2.0 μm long. The nanowire is cooled to a temperature of 13 K, and we assume the electron’s average kinetic energy is that of gas molecules at this temperature ( 3kT/2). (a) What are the three lowest possible energy levels of the electrons? (b) What is the approximate quantum number of electrons moving in the wire?arrow_forward(a) Find the mass density of a proton, modeling it as a solid sphere of radius 1.00 x 10-15 m. (b) What If? Consider a classical model of an electron as a uniform solid sphere with the same density as the proton. Find its radius. (c) Imagine that this electron possesses spin angular momentum Iω = h/2 because of classical rotation about the z axis. Determine the speed of a point on the equator of the electron. (d) State how this speed compares with the speed of light.arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
- Classical Dynamics of Particles and SystemsPhysicsISBN:9780534408961Author:Stephen T. Thornton, Jerry B. MarionPublisher:Cengage Learning
Classical Dynamics of Particles and Systems
Physics
ISBN:9780534408961
Author:Stephen T. Thornton, Jerry B. Marion
Publisher:Cengage Learning