Modern Physics for Scientists and Engineers
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 37P
To determine

Show that an equation giving these wavelengths is: 1λ=R(1nl21nu2) and also find the value of Rydberg constant in this case.

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In 1896 Pickering found lines from the star Zeta Pup- pis that had not been observed on Earth. Bohr showed in 1913 that the lines were due to He+. Show that an equation giving these wavelengths is 1-(2) R( n²/² = λ What value should the Rydberg constant R have in this case? n
Three isotopes of hydrogen occur in nature; ordinary hydrogen, deuterium, and tritium. Their nuclei consist of, respectively, 1 proton, 1 proton and 1 neutron (deuteron), and 1 proton and 2 neutrons (triton). (a) Determine Rydberg constants for deuterium and tritium. (b) Determine the wavelength difference between the Balmer α lines of deuterium and tritium. (c) Determine the wavelength difference between the Balmer α lines of hydrogen and tritium. Note: The difference in this case would be caused by the nuclear mass. In deriving the Bohr atom, the first order of approximation was to assume that the nucleus doesn't move at all. The correction to this can be done by replacing the mass of the electron with the reduced mass of the electron-nucleus system, where, as you studied in mechanics, the reduced mass is given by μ=m1m2/(m1+m2). Additionally, the Balmer series is the one that terminates in the n=2 level with the α line corresponding to the n=3→n=2 transition.
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