Modern Physics
2nd Edition
ISBN: 9780805303087
Author: Randy Harris
Publisher: Addison Wesley
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Chapter 7, Problem 6CQ
To determine
To Explain:If a gas can be too cold to absorb Paschen series and Lyman series lines.
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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?
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.
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At what angle, in degrees, would the first maximum be for the fourth-lowest energy Balmer transition photon, when sent through the slits above?
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Consider a cavity with a volume of 1cc and the
frequency range 0 to 473 THz. Assume a
refractive index of unity. a. What is the total
number of optical modes contained in this
cavity? b. What is the mode density
(modes/k/m3) at 473 THz? c. If a Neon atom is
placed in this cavity which has an emission at
473 THz with a 16 MHz linewidth, how many
modes can the atom couple to? d. How small
would the cavity have to be in order to have
the number of modes coupled to equal 100?
Chapter 7 Solutions
Modern Physics
Ch. 7 - Prob. 1CQCh. 7 - Prob. 2CQCh. 7 - Prob. 3CQCh. 7 - Prob. 4CQCh. 7 - Prob. 5CQCh. 7 - Prob. 6CQCh. 7 - Prob. 7CQCh. 7 - Prob. 8CQCh. 7 - Prob. 9CQCh. 7 - What are the dimensions of the spherical harmonics...
Ch. 7 - Prob. 11CQCh. 7 - Prob. 12CQCh. 7 - Prob. 13CQCh. 7 - Prob. 14CQCh. 7 - Prob. 15CQCh. 7 - Prob. 16CQCh. 7 - Prob. 17ECh. 7 - Prob. 18ECh. 7 - Prob. 19ECh. 7 - Prob. 20ECh. 7 - Prob. 21ECh. 7 - Prob. 22ECh. 7 - Prob. 23ECh. 7 - Prob. 24ECh. 7 - Prob. 25ECh. 7 - Prob. 26ECh. 7 - Prob. 27ECh. 7 - Show that of hydrogen’s spectral seriesLyman,...Ch. 7 - Prob. 29ECh. 7 - Prob. 30ECh. 7 - Prob. 31ECh. 7 - Prob. 32ECh. 7 - Prob. 33ECh. 7 - Prob. 34ECh. 7 - Prob. 35ECh. 7 - Prob. 36ECh. 7 - Prob. 37ECh. 7 - A particle orbiting due to an attractive central...Ch. 7 - Prob. 39ECh. 7 - Prob. 40ECh. 7 - Prob. 41ECh. 7 - Prob. 42ECh. 7 - Prob. 43ECh. 7 - How many different 3d states are there? What...Ch. 7 - Prob. 45ECh. 7 - Prob. 46ECh. 7 - Prob. 47ECh. 7 - Prob. 48ECh. 7 - Prob. 49ECh. 7 - Prob. 50ECh. 7 - Prob. 51ECh. 7 - Prob. 52ECh. 7 - Prob. 53ECh. 7 - Prob. 54ECh. 7 - For states where l=n1 , the radial probability...Ch. 7 - Prob. 56ECh. 7 - Prob. 57ECh. 7 - Prob. 58ECh. 7 - Prob. 59ECh. 7 - Prob. 60ECh. 7 - Prob. 61ECh. 7 - Prob. 62ECh. 7 - Prob. 63ECh. 7 - Prob. 64ECh. 7 - Prob. 65ECh. 7 - Prob. 66ECh. 7 - Prob. 67ECh. 7 - Prob. 68ECh. 7 - Prob. 69ECh. 7 - Prob. 70ECh. 7 - Prob. 71ECh. 7 - Prob. 72ECh. 7 - Prob. 73ECh. 7 - Prob. 74ECh. 7 - Prob. 75ECh. 7 - Prob. 76ECh. 7 - Prob. 77ECh. 7 - Prob. 78ECh. 7 - Prob. 79CECh. 7 - Prob. 80CECh. 7 - Prob. 81CECh. 7 - Prob. 83CECh. 7 - Prob. 84CECh. 7 - Prob. 85CECh. 7 - Prob. 86CECh. 7 - Prob. 87CECh. 7 - Prob. 89CE
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Similar questions
- In hydrogen’s characteristic spectra, each series (Lyman, Balmer, etc) has a “series limit”, where the wavelengths at one end of the series tend to “bunch up”, approaching a single limiting value. part a: Does the infinite well have series limits? If not, why not? If so, is it at the short or long wavelength end?arrow_forwarda) How many ways are there to arrange 3 quanta among 4 atoms in a solid? b) . the ground state energy. What is the Boltzmann factor for this excited state? >At room temperature, the fourth excited state of a microscopic oscillator is o.6 eV abovearrow_forwardA hydrogen atom has energy -1.36 × 10-19 J, and the electron can be in any one of ten different quantum states. Find the spectroscopic notation for this atom.what is the principal quantum number? What is total orbital angular momentum? What is maximum z. Direction total angular momentum? What is degeneracy ?arrow_forward
- Consider the Balmer series discussed in the book (and Prof. Scherer's lecture notes), where the frequencies are given by: x (3.29 × 1015 s-1) n = 3,4,5, .. v = Let us focus only on the spectral lines and transitions corresponding to the Balmer series. a) Suppose the Balmer series of hydrogen is studied using a Franck-Hertz experiment. What is the threshold voltage required for n=3? How about n=4? b) The Lyman Series frequencies are given by v = |1- x (3.29 x 1015 s-1). Describe what is different about these two series of emission frequencies of photons from the hydrogen atom? That is, what distinguishes one series from the other? (Hint: it may help to think about the Bohr model interpretation of transitions.)arrow_forwardFirst consider some simple electronic partition functions: a. Consider a two-level system of N particles separated by an energy of hv. i. Derive expressions for ē, E, and P, as a function of T. P, is the probability that the system is in the higher energy level. ii. What are the limiting values for each of these at T = 0 and kT » hv. iii. For a level spacing 200 cm what is T when Ē = Nhv. iv. What is P, at the T found in part iii?arrow_forwardThe Lennard-Jones parameters for argon are: A = 1.022 x 10-7 J m° and B = 1.579 x 10-134 J m12. Calculate the distance at which the energy will be minimum and calculate the minimum energy. Draw the energy profile also. I.arrow_forward
- 1. Derive the density of states as a function of energy for a purely two-dimensional electron system. Show the result in a graph and compare qualitatively with that for 0, 1 and 3 dimensions (1 page maximum).arrow_forward2. Suppose a particle of mass, m, has energy E, and wave function: WE (x, t = 0) = Aeikx + Be-ikx What is WE(x, t)? Calculate the probability density of the particle when it has the wavefunction, E (x, t). If you wish to simply your answer algebraically, use this information: let A = aeia and B = beif and A = a - B. where the variables a, b, a, ß are all real! WARNING: Simplifying the equation is somewhat time consuming. Show/explain why p(x,t) is not normalizable. According to quantum theory, all physical systems must have an associated wavefunction that is normalizable. Explain why plane wave solutions to Schrodinger's equation are used in quantum theory, despite not being normalizable?arrow_forwardIf a hydrogen atom in the ground state absorbs a 93.7 nm photon, corresponding to a transition line in the Lyman series, how does this affect the atom's energy and size? How much energy is needed to ionize the atom when it is in this excited state? Give your answers in absolute units, and relative to the ground state. (the Lyman series is a hydrogen spectral series of transitions and resulting ultraviolet emission lines of the hydrogen atom as an electron goes from n ≥ 2 to n = 1 (where n is the principal quantum number), the lowest energy level of the electron.)arrow_forward
- la) The maximum value of the Planck spectrum for 91 photons at 6 Kelvin is (k=Boltzmann constant) Select one: O a. 182.00 Ob. 16.92k Oc. 546.00 O d. zero Oe. 91.00 b) A box contains 3 identical fermions. What is the partition function if each particle can occupy any of 10 single- particle states? Assume that the energy for each of these states is zero. Select one: O a. 1 Ob. 495.00 Oc. 100 Od. zero Oe. infinityarrow_forward1. Cannot be! Imagine a certain kind of particle, such that each single-particle state can be occupied by at most M particles, with M > 1. For M = 1 and M = ∞, we recover the usual fermion and boson cases. We will focus on the case when the particles do not interact with each other, and the single particle quantum states i have energies e¿. Assume that the system is in equilibrium at temperature T and chemical potential μ. (a) (b) (c) above. Calculate the appropriate partition function for the system in the conditions discussed Compute, as a function of temperature and chemical potential, the average occupation number (n) for state i, and find simplified expressions in the low and high temperature limits. For M1, does the system have the analog of a Fermi energy, i.e. an energy at which the occupation number is discontinuous at T = 0?arrow_forward6. Diffraction ffect of Josephson junction. Consider a junction of rectangular cross section with a magnetic field B applied in the plane of the junction, normal to an edge of width te. Let the thickness of the junction be T. Assume for convenience that the phase difference of the two superconductors is m2 when B 0. Show that the de current in the presence of the magnetic field is sin(uTBellic) J-Jo (wTBelhe)arrow_forward
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