Modern Physics For Scientists And Engineers
2nd Edition
ISBN: 9781938787751
Author: Taylor, John R. (john Robert), Zafiratos, Chris D., Dubson, Michael Andrew
Publisher: University Science Books,
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Chapter 5, Problem 5.19P
To determine
(a)
Show that alternate lines of Balmer series of
To determine
(b)
Show that all lines of
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Some of the most powerful lasers are based on the energy levels of neodymium in solids, such as glass, as shown . (a) What average wavelength light can pump the neodymium into the levels above its metastable state? (b) Verify that the 1.17 eV transition produces1.06 μm radiation.
Use the Rydberg equation to calculate the wavelength (in nm) of the hydrogen Balmer series line having nouter = 5 and ninner = 2. After calculating delta E, take the absolute value, and solve for frequency using Equation (1). Use this frequency in Equation (2) to solve for the wavelength.Express your answer to 3 significant figures.
2.11 (a) By using the deBroglie relation, derive the Bohr condition mvr = nħ for
the angular momentum of an electron in a hydrogen atom.
(b) Use this expression to show that the allowed electron energy states in
hydrogen atom can be written
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Chapter 5 Solutions
Modern Physics For Scientists And Engineers
Ch. 5 - Prob. 5.1PCh. 5 - Prob. 5.2PCh. 5 - Prob. 5.3PCh. 5 - Prob. 5.4PCh. 5 - Prob. 5.5PCh. 5 - Prob. 5.6PCh. 5 - Prob. 5.7PCh. 5 - Prob. 5.8PCh. 5 - Prob. 5.9PCh. 5 - Prob. 5.10P
Ch. 5 - Prob. 5.11PCh. 5 - Prob. 5.12PCh. 5 - Prob. 5.13PCh. 5 - Prob. 5.14PCh. 5 - Prob. 5.15PCh. 5 - Prob. 5.16PCh. 5 - Prob. 5.17PCh. 5 - Prob. 5.18PCh. 5 - Prob. 5.19PCh. 5 - Prob. 5.20PCh. 5 - Prob. 5.21PCh. 5 - Prob. 5.22PCh. 5 - Prob. 5.23PCh. 5 - Prob. 5.24PCh. 5 - Prob. 5.25PCh. 5 - Prob. 5.26PCh. 5 - Prob. 5.27P
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- Some of the most powerful lasers are based on the energy levels of neodymium in solids, such as glass, as shown in Figure below. (a) What average wavelength light can pump the neodymium into the levels above its metastable state? .(b) Verify that the 1.17 eV transition produces 1.06 micrometre radiation.arrow_forward6.46 Atoms with very high quantum numbers, so that the atom is laboratory sized, are known as Rydberg atoms. (a) What would be the quantum number of a hydrogen atom with a radius of 1 um? (b) What would be the ionization energy of this atom? (c) What would be the wavelength of the transition to the next lowest level?arrow_forwarda) 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?arrow_forward
- Problem 2. Calculate the wavelength of light emitted in the 2P/2 1S/2 transition of the real hydrogen atom (in- cluding the fine structure correction). The values of the quantum numbers n, I and j follow from the spectroscopic notation nL, and the letters S, P,D and F corresponds to l = 0, 1,2, 3 respectively. Spin value is always 1/2 for the hydrogen atom. Express your answer in Angstroms.arrow_forwardConsider 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_forward(a) Suppose you have solved the Schrödinger equation for the singly- ionized helium atom and found a set of eigenfunctions N(r). (1) How do the N(r) compare with the hydrogen atoin wave functions? (2) If we include a spin part o+ (or o-) for spin up (or spin down), how do you combine the o's and o's to form an eigenfunction of definite spin? (1)) Now consider the helium atom to have two electrons, but ignore the clectromagnetic interactions between them. (1) Write down a typical two-electron wave function, in terms of the d's aund o's, of definite spin. Do not choose the ground state. (2) What is the total spin in your example? (3) Demonstrate that your example is consistent with the Pauli exclu- sion principle. (4) Demonstrate that your cxample is antisyınnietric with respect to clectron interchange.arrow_forward
- Write down Balmer formula and explain the terms involved, what is the wavelength ofthe light emitted when the electron in a hydrogen atom jumps from n2 = 4 to n1 = 1levels? (Rydberg Constant R = 109677 cm–1).arrow_forwardif the chlorine molecule at 290K were to rotate at the angular frequency predicted by the equipartition theorem what would be the average centipital force ? ( the atoms of Cl are 2 x 10-10 m apart and the mass of the chlorine atom 35.45 a.m.u )arrow_forwardA laser system is capable of lasing at several infrared wavelengths where the most prominent wavelengths where the most prominent wavelengths is 3.1235nm. (Given k=8.6* 10^-5 ev/k or 1.38* 10^-23 J/K a) What would be the difference(in ev)between upper and lower levels for this wavelengths ? b) The relative population of these states at 27degree C is c) Which states is occupied by atoms under conditions of thermal equilibrium ? d) The relative population of these states at 40degree C is e) What would be the difference(in J)between upper and lower levels for this wavelengths ?arrow_forward
- Using the Rydberg formula, find the wavelength of the line in the Balmer series of the hydrogen spectrum for m = 5. The value of Rydberg constant is 1.097 × 107 m–1 and n = 2 for the Balmer series. (Round the final answer to the nearest whole number.) The wavelength is _______nm.arrow_forwardThis question concerns the addition of 3 angular momenta (as covered in the tutorial). Consider again the hydrogen atom including the nuclear spin (1= 1/2). For an electron in a 3d level, what are all the possible values for the total angular momentum quantum number (including electron spin, nuclear spin and orbital motion)? Select an answer and submit. For keyboard navigation, use the up/down arrow keys to select an answer. a b с d e 1,2,3 0,1,2,3 3/2,5/2 1,3/2,2,5/2,3 1,3arrow_forwardThe charge density of the electron cloud of the hydrogen atom is -4-2r/a Pe(r) (1) Ta3 with q > 0 the charge of the proton, and a is the Bohr radius. Compute the polar- izability of the hydrogen atom. Use the approximation of Example 4.1. ASsume the electron cloud is unchanged, but is displaced relative to the proton by -d = -dk with |d < a by an external electric field Eo = Eok. Then, in equilibrium, the force on the proton is F, = 0 = q [E, + E.(d)] (2) where Ee(d) is the electric field created at position d by just the electron charge density Pe(r) (tacking origin of the spherical coordinate system still at the center of the electron charge distribution). Hence use Gauss' Law to find the electric field created by the electron charge density, and then expand your result in powers of d/a 1.arrow_forward
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