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The Rydberg-Ritz combination principle is an empirical relationship proposed by Walter Ritz in 1908 to explain the relationship among spectral lines of the hydrogen atom. The principle states that the spectral lines of the atom include frequencies that are either the sum or the difference of the frequencies of two other lines. This principle is obvious to us, because we now know that spectra arise from transitions between energy levels, and the energy of a transition is proportional to the frequency.
The frequencies of the first ten lines of an emission spectrum of hydrogen are given in the table at the bottom of this page. In this problem, use ideas from this chapter to identify the transitions involved, and apply the Rydberg-Ritz combination principle to calculate the frequencies of other the spectrum of hydrogen.
a. Use Balmers original equation,
b. Use the expression you derived in (a) to calculate the expected ratio of the frequencies of the first two lines in each of the Lyman, Balmer, and Paschen series: (for the Lyman series); (for the Balmer series); and (for the Paschen series). Compare your calculated ratios to the observed ratio 2.465263/2.921793 = 0.843750 to identity the series as the Lyman, Balmer, or Paschen series. For each line in the series, specify the transition (quantum numbers) involved. Use a diagram, such as that given in Figure 8-13 to summarize your results.
c. Without performing any calculations, and starting from the Rydberg formula, equation (8.4), show that
d. Use the Rydberg-Ritz combination principle to determine, if possible, the frequencies for the other two series named in (b). (Hint The diagram you drew in part (b) might help you density the appropriate combinations of frequencies.)
e. Identify the transition associated with a of frequency
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Chapter 8 Solutions
General Chemistry: Principles and Modern Applications (11th Edition)
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- An FM radio station found at 103.1 on the FM dial broadcasts at a frequency of 1.031188s1 (103.1 MHz). What is the wavelength of these radio waves in meters?arrow_forwardAccording to a relationship developed by Niels Bohr, for an atom or ion that has a single electron, the total energy, En, of an electron in a stable orbit of quantum number n is En = [Z2/n2] (2.179 1018 J) where Z is the atomic number. Calculate the ionization energy for the electron in a ground-state He+ ion.arrow_forwardThis laser emits green light with a wavelength of 533 nm. (a) What is the energy, in joules, of one photon of light at this wavelength? (b) If a particular laser produces 1.00 watt (W) of power (1 W = 1 J/s), how many photons are produced each second by the laser?arrow_forward
- RGB color television and computer displays use cathode ray tubes that produce colors by mixing red, green, and blue light. If we look at the screen with a magnifying glass, we can see individual dots turn on and off as the colors change. Using a spectrum of visible light, determine the approximate wavelength of each of these colors. What is the frequency and energy of a photon of each of these colors?arrow_forwardCalculate the wavelength of the Balmer line of the hydrogen spectrum in which the initial n quantum number is 5 and the final n quantum number is 2.arrow_forward
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