An Introduction to Thermal Physics
1st Edition
ISBN: 9780201380279
Author: Daniel V. Schroeder
Publisher: Addison Wesley
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Chapter A.1, Problem 3P
To determine
To Show: The de Broglie relation using Einstein relation.
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Consider an electron with kinetic energy E = 10 eV. Calculate the de Broglie wavelength of the electron. Express your answer in Angstroms. 1 Angstrom = 1 x 10-10 m.
A nonrelativistic particle of mass m and charge q is accelerated from rest through a potential difference Delta V. (a) Use conservation of energy to find a symbolic expression for the momentum of the particle in terms of m, q, and DV. (b) Write a symbolic expression for the de Broglie wavelength using the result of part (a). (c) If an electron and proton go through the same potential difference but in opposite directions, which particle will have the shorter wavelength?
Calculate the de Broglie wavelength of(a) a 50.0 kg woman jogging leisurely at 2.0 m/s,(b) a free electron with kinetic energy 2.0 MeV, and(c) a free electron with kinetic energy 20 eV.Use the proper relativistic expression when necessary.
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An Introduction to Thermal Physics
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- A) Calculate the de Broglie wavelength of a neutron (mn = 1.67493×10-27 kg) moving at one six hundredth of the speed of light (c/600). Enter at least 4 significant figures. (I got the answer 949.4 pm but it is wrong, please help) B) Calculate the velocity of an electron (me = 9.10939×10-31 kg) having a de Broglie wavelength of 230.1 pm.arrow_forwardShow that Ψ(x,t)=Ae^i(kx−ωt) is a valid solution to Schrӧdinger’s time-dependent equation.arrow_forwardIt is stated in the text that special relativity must be used to calculate the de Broglie wavelength of electrons in an electron microscope. Let us discover how much of an effect relativity has. Consider an electron accelerated through a potential difference of 1.00 x 105 V.a. Using the Newtonian (nonrelativistic) expressions for kinetic energy and momentum, what is the electron’s de Broglie wavelength?b. The de Broglie wavelength is λ = h/p, but the momentum of a relativistic particle is not mv. Using the relativistic expressions for kinetic energy and momentum, what is the electron’s de Broglie wavelength?arrow_forward
- For a free electron, determine the electron's de broglie wavelength, momentum, kinetic energy and speed when k = 50 nm-1.arrow_forwardCalculate the de Broglie wavelength of a bullet of mass 80 g travelling at speed 869 m/s. Express your answer as λ x 10-35 m and type in just the value of λ. Use three decimals in your answer.arrow_forwardWPS Office ASSIGNMENT 2.pdf + Sign in O Go Premium = Menu v Home Insert Comment Edit Page Protect Tools 1. The photoelectric threshold wavelength of a tungsten surface is 270 nm. Calculate the maximum kinetic energy (in eV) of the electrons ejected from this tungsten surface by ultraviolet radiation of frequency 1.45 x 1015 Hz. K 2. What would the min. work function for a metal have to be for visible light (380–750 nm) to eject photoelectrons? B 3. The cathode-ray tubes that generated the picture in early color televisions were sources of X-rays. If the acceleration voltage in a television tube is 15 kV, what are the shortest- wavelength x-rays produced by the television? 4. (a) What is the minimum potential difference between the filament and the target of an x- ray tube if the tube is to produce x-rays with a wavelength of 0.16 nm? (b) What is the shortest wavelength produced in an x-ray tube operated at 30 kV? 3E 5. A laser produces light of wavelength 620 nm in an ultrashort pulse.…arrow_forward
- Draw a graph showing the variation of de Broglie wavelength λ of a particle of charge q and mass m, with the accelerating potential V. An α-particle and a proton have the same de-Broglie wavelength equal to 1Å. Explain with calculations, which of the two has more kinetic energy.arrow_forwardAn electron has energy E = 4?₀ in the regions where it has a potential as shown in the figure below. Considering the regions x > L (region 1) and 0 < x < L (region 2). What will be the ratio between the Broglie wavelengths of the electron in regions 1 and 2, that is, λ₁/λ₂ ?The potential energy is zero within the range 0<x<L and has a constant value Uo outside it.arrow_forward(a) What is the de Broglie wavelength (in m) of a proton moving at a speed of 3.30 × 104 m/s? 1.2E-11 m (b) What is the de Broglie wavelength (in m) of a proton moving at a speed of 1.92 × 108 m/s? Note that the proton is moving very close to the speed of light in this case. Therefore, we cannot use the non-relativistic approximation for momentum. What is the relativistic relationship between momentum and speed? What is the gamma factor? m (c) What is the de Broglie wavelength for an electron having a kinetic energy of 3.15 MeV? X Your response differs from the correct answer by more than 10%. Double check your calculations. marrow_forward
- Consider the Bohr model of the doubly ionized lithium ion (3 protons) with a single electron. The ground state energy is -122.4 ev What is the kinetic energy for the electron in orbit? eV Write down the relationship between the kinetic energy K, the momentump and the mass m K= write your answer as a formula, e.g. z=x^4/3y Use these to find the de Broglie wavelength of the electron in this orbit: The de Broglie wavelength is nm If the electron is actually a standing wave, what radius does this suggest for the electron's orbit? ro = nm Assuming classical uniform circular motion for the electron in the Coulomb potential at the radius computed above, what is the total energy of the atom? The potential energy is Oze?/(4tte ro) Ze2/ (4πε ro) O-ze?/(8te ro) Oze/ (8πε r0) The kinetic energy is Οze2/ (4πε r0 ) Ο-Ze2/ (4πε r0) O-Ze2/(8ne r0) Οze2/ (8πε r0) The total energy is Oze2/ (4πε r ) O-Ze2/(4ne r0) O-Ze2/(8te r0) OZe2/ (8πε r0) Hence the total energy is evarrow_forwardPART A: A metal surface is illuminated with photons with a frequency f=1.5×10^15 Hz. The stopping potential for electrons photoemitted from the surface is 3.6 V. What is the work function of the metal? Answer= 2.6 eV PART B: A certain metal has a work function ϕ. What is the maximum photon wavelength that will produce photoemission? Express your answer in terms of ϕ,Planck's constant h, and the speed of light c. *Please answer Part B*arrow_forwardA beam of electrons is accelerated from rest through a potential difference of 0.100 kV and then passes through a thin slit. When viewed far from the slit, the diffracted beam shows its first minimum at ± 14.6° from the original direction of the beam. A) What is the velocity of the electrons? B) What is the de Broglie wavelength of the electrons?arrow_forward
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