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 5.12P
To determine
The range of wavelength in Lyman, Balmer and Paschen series of Hydrogen and also show that the lines in the Lyman series are all in the UV region, those of Paschen in the IR region and Balmer series in the visible and the UV region and also show that the series do not overlap one another but that the next series, in which the lower level is
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The visible lines of the Balmer series were observed first because they are most easily seen. Show that the wavelengths of spectral lines in the Lyman (n = 1) and Paschen (n = 3) series are not in the visible region. Find the wavelengths of the four visible atomic hydrogen lines. Assume the visible wavelength region is λ = 400– 700 nm.
Compute 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)Δλ
The wavelengths of the Lyman series for hydrogen are given by = RH(1-2), = 2, 3, 4, ...
1/2
(a) Calculate the wavelengths of the first three lines in this series.
nm
nm
nm
(b) Identify the region of the electromagnetic spectrum in which these lines appear.
O ultraviolet region
O infrared region
O x-ray region
O visible light region
O gamma ray region
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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- When the absorption spectrum of hydrogen at room temperature is analyzed, absorption lines for the Lyman series are found, but none are found for the Balmer series. What does this tell us about the energy state of most hydrogen atoms at room temperature?arrow_forwardIn extreme-temperature environments, such as those existing in a solar corona, atoms may be ionized by undergoing collisions with other atoms. One example of such ionization in the solar corona is the presence of C5+ ions, detected in the Fraunhofer spectrum. (a) By what factor do the energies of the C5+ ion scale compare to the energy spectrum of a hydrogen atom? (b) What is the wavelength of the first line in the Paschen series of C5+ ? (c) In what part of the spectrum are these lines located?arrow_forwardThe Balmer series for hydrogen was discovered before either the Lyman or the Paschen series. Why?arrow_forward
- (a) If one subshell of an atom has nine electrons in it, what is the minimum value of (b) What is the spectroscopic notation for this atom, if this subshell is part of the n = 3 shell?arrow_forwardThe work function for potassium is 2.26 eV. What is the cutoff frequency when this metal is used as photoelectrode? What is the stopping potential when for the emitted electrons when this photo electrode is exposed to radiation of frequency 1200 THz?arrow_forwardSingly ionized helium has a single orbiting electron, so the mathematicsof the Bohr hydrogen atom will apply, with one important difference: The charge of the nucleus is twice that of the single proton at the center of a hydrogen atom. This changes the energy levels; the magnitude of each energy is greater than the corresponding Bohr level by a factor of 22 = 4: The Balmer and Lyman series of spectral lines in hydrogen have analogs in singly ionized helium, but at shorter wavelengths; the photons corresponding to these transitions are beyond the visiblelight spectrum. The transitions that end on the n = 4 state produce a set of spectral lines called the Pickering series. The visible-light lines in this series were first seen in the light from certain hot stars, but some of the lines overlap the hydrogen Balmer series lines, so these lines were initially missed. This led to an initial mischaracterization of the source of the lines. The Paschen series of wavelengths in the hydrogen…arrow_forward
- Singly ionized helium has a single orbiting electron, so the mathematicsof the Bohr hydrogen atom will apply, with one important difference: The charge of the nucleus is twice that of the single proton at the center of a hydrogen atom. This changes the energy levels; the magnitude of each energy is greater than the corresponding Bohr level by a factor of 22 = 4: The Balmer and Lyman series of spectral lines in hydrogen have analogs in singly ionized helium, but at shorter wavelengths; the photons corresponding to these transitions are beyond the visiblelight spectrum. The transitions that end on the n = 4 state produce a set of spectral lines called the Pickering series. The visible-light lines in this series were first seen in the light from certain hot stars, but some of the lines overlap the hydrogen Balmer series lines, so these lines were initially missed. This led to an initial mischaracterization of the source of the lines. What is, approximately, the longest wavelength that…arrow_forwardSingly ionized helium has a single orbiting electron, so the mathematicsof the Bohr hydrogen atom will apply, with one important difference: The charge of the nucleus is twice that of the single proton at the center of a hydrogen atom. This changes the energy levels; the magnitude of each energy is greater than the corresponding Bohr level by a factor of 22 = 4: The Balmer and Lyman series of spectral lines in hydrogen have analogs in singly ionized helium, but at shorter wavelengths; the photons corresponding to these transitions are beyond the visiblelight spectrum. The transitions that end on the n = 4 state produce a set of spectral lines called the Pickering series. The visible-light lines in this series were first seen in the light from certain hot stars, but some of the lines overlap the hydrogen Balmer series lines, so these lines were initially missed. This led to an initial mischaracterization of the source of the lines. What energy is required to remove the remaining…arrow_forwardSingly ionized helium has a single orbiting electron, so the mathematicsof the Bohr hydrogen atom will apply, with one important difference: The charge of the nucleus is twice that of the single proton at the center of a hydrogen atom. This changes the energy levels; the magnitude of each energy is greater than the corresponding Bohr level by a factor of 22 = 4: The Balmer and Lyman series of spectral lines in hydrogen have analogs in singly ionized helium, but at shorter wavelengths; the photons corresponding to these transitions are beyond the visiblelight spectrum. The transitions that end on the n = 4 state produce a set of spectral lines called the Pickering series. The visible-light lines in this series were first seen in the light from certain hot stars, but some of the lines overlap the hydrogen Balmer series lines, so these lines were initially missed. This led to an initial mischaracterization of the source of the lines. The longest wavelength in the hydrogen Balmer series…arrow_forward
- Show that the following 4 lines in the Lyman series can be predicted: 91.127, 97.202, 102.52, and 121.57 nm.arrow_forwardThe shortest wavelength of the hydrogen Lyman series is 91.13 nm. Find the three longest wavelengths in this series.arrow_forward(a) What is the wavelength of light for the least energetic photon emitted in the Balmer series of the hydrogen atom spectrum lines? (b) What is the wavelength of the series limit?arrow_forward
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