Modern Physics
2nd Edition
ISBN: 9780805303087
Author: Randy Harris
Publisher: Addison Wesley
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Chapter 7, Problem 28E
Show that of hydrogen’s spectral series−Lyman, Balmer, Paschen, and so on−only the four Balmer lines of Section 7.3 are in visible range (400−700 nm).
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Take h to have an exact value of
6.63 x 10-34 J-s for significant figure purposes,
and use hc = 1.24 x 10³ eV nm (three
significant figures).
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If the electron in a hydrogen atom is to make a transition from the first excited state to the
second excited state, what frequency of photon is needed?
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Calculate the shortest and longest
wavelengths of Balmer series of hydrogen
atom. Given R = 1.097 × 107m1.
Consider a hydrogen atom in the following state:
Pn.e.j.m, = P,,33 = R21(r) Y33
P2.1
With the generalized spherical harmonic given by
e ± m, + 1/2
e7m, + 1/2
Y
Y
1 X+ +
E.m2
X-
28 + 1
2e + 1
= (in units of h) Choose.
= (in units of h) Choose...
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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- Hydrogen gas can be placed inside a strong magnetic field B=12T. The energy of 1s electron in hydrogen atom is 13.6 eV ( 1eV= 1.6*10 J ). a) What is a wavelength of radiation corresponding to a transition between 2p and 1s levels when magnetic field is zero?arrow_forwardWhat is the value of n in the Balmer series for which the wavelength is 410.2 nm. If a hydrogen atom in the ground state absorbs a photon of energy 12.09 eV, to which state will the electron make a transition?arrow_forwardZirconium (Z = 40) has two electrons in an incomplete d subshell. (a) What are the values of n and ℓ for each electron? n = ℓ = (b) What are all possible values of m and ms? m = − to + ms = ± (c) What is the electron configuration in the ground state of zirconium? (Use the first space for entering the shorthand element of the filled inner shells, then use the remaining for the outer-shell electrons. Ex: for Manganese you would enter [Ar]3d54s2)arrow_forward
- 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?arrow_forwardA) What is the least amount of energy, in electron volts, that must be given to a hydrogen atom which is initially in its ground level so that it can emit the HαHα line in the Balmer series? Express your answer in electronvolts to three significant figures. B) How many different possibilities of spectral-line emissions are there for this atom when the electron starts in the n = 3 level and eventually ends up in the ground level?arrow_forwardCompute the oscillation frequency of the electron and the expected absorption or emission wavelength in a Thomson- model hydrogen atom. Use R = 0.053 nm.arrow_forward
- How many electrons can occupy the system with l=0, l=2 and l=4. What is number of possibleorientations of the orbital angular momentum with l=4? What is the smallest z-component of theorbital angular momentum?arrow_forwarda) The Balmer series consists of transitions in hydrogen from higher states where n > 2 tothe n = 2 state. Use the Bohr model to show each ‘line’ in the Balmer series can bedescribed by the following equation;1/λ = R(1/22 -1/n2) where the Rydberg Constant R = me4/8εo2 h3cb) Use this result to confirm the wavelength of light emitted in the Hα transition.c) Develop similar equations for the Lyman, Paschen, Brackett and Pfund spectral serieswhere where the final states are n= 1, 3, 4 and 5 respectively.d) What is the wavelength of light emitted from hydrogen in a transition from the n = 3energy level to n = 1? In which region of the electromagnetic spectrum is this light found?In which spectral series? What colour of light is observed?arrow_forwardХ SA2. For a certain electronic state in hydrogen, the angular part of the wave function is (0) = C sin cos 0. Is the electron described by this wave function most likely to be found close to the z axis, close to the xy plane, or somewhere in between? EXPLAIN YOUR ANSWER. (0 is the polar angle between r and the z axis.)arrow_forward
- The 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_forwardWhat is the longest - wavelength line in nanometers in the infrared series for hydrogen where m = 3?arrow_forwardCompute the intrinsic line-width (Δλ) of the Lyman α line (corresponding to the n=2 to n=1) transition for the Hydrogen atom. You may assume that the electron remains in the excited state for a time of the order of 10^−8s. The line-width may be computed using:ΔE=(hc/λ^2)Δλarrow_forward
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