Modern Physics for Scientists and Engineers
4th Edition
ISBN: 9781133103721
Author: Stephen T. Thornton, Andrew Rex
Publisher: Cengage Learning
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Chapter 4, Problem 19P
To determine
Prove one of the Ritz combination rule
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1.5
The time-averaged potential of a neutral hydrogen atom is given by
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ao/2, ao being the
Use the Rydberg equation, to calculate the frequency (in s–1), of the Balmer series line for hydrogen where nouter = 3 and ninner = 2. First, use the Rydberg equation to calculate delta E; use the absolute value of delta E in equation (1) to solve for the frequency.Express your answer to 3 significant figures.
a) Calculate the energy of the emissive transition with the lowest energy possible for the Lyman series, for a mole of hydrogen atoms. Express your answer in joules/mol.
b) Is this transition in the visible spectral domain? If not, in which region is it located?
Chapter 4 Solutions
Modern Physics for Scientists and Engineers
Ch. 4 - Prob. 1QCh. 4 - Prob. 2QCh. 4 - Prob. 3QCh. 4 - Prob. 4QCh. 4 - Prob. 5QCh. 4 - Prob. 6QCh. 4 - Prob. 7QCh. 4 - Prob. 8QCh. 4 - Prob. 9QCh. 4 - Prob. 10Q
Ch. 4 - Prob. 11QCh. 4 - Prob. 12QCh. 4 - Prob. 13QCh. 4 - Prob. 2PCh. 4 - Prob. 3PCh. 4 - Prob. 4PCh. 4 - Prob. 5PCh. 4 - Prob. 6PCh. 4 - Prob. 7PCh. 4 - What fraction of 5-MeV α particles will be...Ch. 4 - Prob. 9PCh. 4 - Prob. 10PCh. 4 - Prob. 11PCh. 4 - Prob. 12PCh. 4 - Prob. 13PCh. 4 - Prob. 14PCh. 4 - Prob. 15PCh. 4 - Prob. 16PCh. 4 - Prob. 17PCh. 4 - Prob. 18PCh. 4 - Prob. 19PCh. 4 - Prob. 20PCh. 4 - Prob. 21PCh. 4 - Prob. 22PCh. 4 - Prob. 23PCh. 4 - Prob. 24PCh. 4 - Prob. 25PCh. 4 - Prob. 26PCh. 4 - Prob. 27PCh. 4 - Prob. 28PCh. 4 - Prob. 29PCh. 4 - Prob. 30PCh. 4 - Prob. 31PCh. 4 - Prob. 32PCh. 4 - Prob. 33PCh. 4 - Prob. 34PCh. 4 - Prob. 35PCh. 4 - Prob. 36PCh. 4 - Prob. 37PCh. 4 - Prob. 38PCh. 4 - Prob. 39PCh. 4 - Prob. 40PCh. 4 - Prob. 41PCh. 4 - Prob. 42PCh. 4 - Prob. 43PCh. 4 - Prob. 44PCh. 4 - Prob. 45PCh. 4 - Prob. 46PCh. 4 - Prob. 47PCh. 4 - Prob. 48PCh. 4 - Prob. 49PCh. 4 - Prob. 50PCh. 4 - Prob. 51PCh. 4 - Prob. 52PCh. 4 - Prob. 54PCh. 4 - Prob. 55PCh. 4 - Prob. 56PCh. 4 - Prob. 57PCh. 4 - Prob. 59PCh. 4 - Prob. 60PCh. 4 - Prob. 61P
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- The wavelengths of the Paschen series for hydrogen are given by n = 4, 5, 6, ... (a) Calculate the wavelengths of the first three lines in this series. 1.877e-6 Your response differs significantly from the correct answer. Rework your solution from the beginning and check each step car 1.283e-6 Your response differs significantly from the correct answer. Rework your solution from the beginning and check each step car 1.905e-6 Your response differs significantly from the correct answer. Rework your solution from the beginning and check each step car (b) Identity the region of the electromagnetic spectrum in which these lines appear. O visible light region O ultraviolet region O infrared region O gamma ray region O x-ray regionarrow_forward4.8. Solve Schrödinger's equation for the ground state of helium neglecting the potential term between the two electrons. What is the energy of the ground state calculated this way? The measured value is -24.6 eV. What do you think the difference is caused by? Give an explanation in physical terms.arrow_forward6.1.5. Radiation has been detected from space that is characteristic of an ideal radiator at T = 2.728 K. (This radiation is a relic of the Big Bang at the beginning of the universe.) For this temperature, at what wavelength does the Planck distribution peak? In what part of the electromagnetic spectrum is this wavelength? %3Darrow_forward
- Photons from the Balmer series of hydrogen transitions are sent through a double slit. What must be the distance between the slits such that the lowest energy Balmer transition has a first-order maximum (maximum adjacent to the central maximum) at an angle of 2.00°? Express your answer in um. Type your answer... At what angle, in degrees, would the first maximum be for the fourth-lowest energy Balmer transition photon, when sent through the slits above? Type your answer... DOD Submitarrow_forwardWhat is the Born interpretation of the wave function? Use formula, where applicable. Given that a solution to Schrodinfer Equation (SE) is: Y = eikx=coskx + i sin kx, where k = (2mE/h2)1/2arrow_forwardThe three lowest energy levels of a hydrogen atom are -13.6 eV, -3.4 eV, and -1.5 eV. Place this atom in thermal contact with a reservoir and assume that there is only one way to occupy any one of these levels. Calculate the relative probability that this hydrogen atom at T = 316 K is in its first excited state (at -3.4 eV) relative to its ground state (at -13.6 eV). Write your answer in exponential form. An "eV" (electron volt) is the energy acquired by an electron accelerated across a 1 volt potential difference. This unit is used to describe electronic energy levels in atoms or solids (semiconductors, etc.). 1 eV = 1.602 x 10-19 J and Boltzmann's constant can be written as 8.617 x 10-5 eV K-1. If your calculator is unable to do this calculation try the web site https://www.wolframalpha.com In this site ex is entered as e^x, though exp(x) can also be used. If you haven't used this website before, a convenient tutorial can be found on youtube (for example,…arrow_forward
- 2 A.) FOR TWO OBSERVABLES A=x %3D B= LZ, FIND THE UNCERTAINTY RELATIONS TA Jo. AND B.) FOR THE STATE Ynim IN A HYOROGEN ATOM, FIND 8. USE THE DEFINITION OF STANDARD DEVIATION.arrow_forwardProblem 4.2 According to quantum mechanics, the electron cloud for a hydrogen atom in the ground state has a charge density. –2r/a p(r) = where q is the charge of the electron and a is the Bohr radius. Find the atomic polarizability of such an atom. [Hint: First calculate the electric field of the electron cloud, Ee(r); then expand the exponential, assuming r « a. For a more sophisticated approach, see W. A. Bowers, Am. J. Phys. 54, 347 (1986).]arrow_forwardCompute linear density value for [111] direction for silver (Ag) R= .144nm. Express your answer in nm-1. Round off the answer to three significant figures. Particulalrly looking for an explaination as to what length equation should be used for [111].arrow_forward
- 4, 3. Excited Ground state 1(ground state) state 4. 4.85E-19 J 4.42E-19 J 3.98E-19 J 3. 1. 3.03E-19 J 2. 1. 1 (ground state) Energy Energy paquosqe emitted 2) [30] Energy Levels Above is a schematic of a Hydrogen atom with its first 5 energy levels. On the right is the energy emitted from the transitions (lines pointing down on the diagram). Using the knowledge that energy and wavelength are hc, connected ( E =) you will figure out the wavelength for each of these %3D transitions. %3D E. h = Planck constant = 6.63E-34 J*s c = speed of light = 3E8 m/s 2 = wavelength in meters E = energy in Joules (J) %3D hc %3D E will be in meters! Divide by 10-9 for nm If you need help converting this to a color easier, try this website once you get the wavelength in nm: https://academo.org/demos/wavelength-to- colour-relationship/arrow_forward475 cm /volt-s, and E, = 1.1 eV, 6? Given these data for Si: 4, = 1350 cm/volt-s, H calculate the following. a) The lifetimes for the electron and for the hole. b) The intrinsic conductivity a at room temperature. c) The temperature dependence of o, assuming that electron collision is dominated by phonon scattering, and plot log o versus 1/T. %3D 7. Repeat Problem 6 for Ge, using Tables 6 L and 6 ?arrow_forwardI need help with problem 4.12 (see picture). This problem involves gamma ray detectors. Problem 4.10: Calculate the amplitude of the voltage pulse produced by collecting a charge equal to that carried by 10^6 electrons on a capacitance of 100pF. (e=1.602x10^-19 C). Thank you.arrow_forward
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