Inorganic chemistry (Gary L. Miessler)
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2.1
Determine the de Broglie wavelength of
a. an electron moving at 1/10 the speed of light.
b. a 400 g Frisbee moving at 10 km/h.
c. an 8.0-pound bowling ball rolling down the lane with a velocity of 2.0 meters per second.
d. a 13.7 g hummingbird flying at a speed of 30.0 miles per hour.
(※ 참고: h = 6.626 x 10^-34 J s, electron mass = 9.110 x 10^-31 kg, light velocity = 2.998 x 10^8 m/s,
lb = 0.4536 kg
풀이:
2.2
Using the equation, determine the energies and wavelengths of the visible emission bands in the atomic spectrum of hydrogen arising from nh = 4, 5, and 6. (The red line, corresponding to nh = 3, was calculated in Exercise 2.1 .)
(※ 참고: RH = 2.179 x 10^-18 J, h = 6.626 x 10^-34 J s, 빛의 속도 c = 2.998 x 10^8 m/s
풀이:
2.3
The transition from the n = 7 to the n = 2 level of the hydrogen atom is accompanied by the emission of radiation slightly beyond the range of human perception, in the ultraviolet region. Determine the energy and wavelength.
풀이:
2.4
Emissions are observed at wavelengths of 383.65 and 379.90 nm for transitions from excited states of the hydrogen atom to the n = 2 state. Determine the quantum numbers nh for these emissions.
풀이:
2.5
What is the least amount of energy that can be emitted by an excited electron in a hydrogen atom falling from an excited state directly to the n = 3 state? What is the quantum number n for the excited state? Humans cannot visually observe the photons emitted in this process. Why not?
풀이:
2.6
Hydrogen atom emission spectra measured from the solar corona indicated that the 4 s orbital was 102823.8530211 cm-1, and 3 s orbital 97492.221701 cm-1, respectively, above the 1 s ground state. (These energies have tiny uncertainties, and can be treated as exact numbers for the sake of this problem.) Calculate the difference in energy (J) between these levels on the basis of these data, and compare this difference to that obtained by the Balmer equation in Section 2.1.2. How well does the Balmer equation work for hydrogen? (Data from Y. Ralchenko, A. E. Kramida, J. Reader, and NIST ASD Team (2011). NIST Atomic Spectra Database (ver. 4.1.0), [Online]. Available: http:// physics.nist.gov/ asd [2012, January 18]. National Institute of Standards and Technology, Gaithersburg, MD.)
풀이:
2.7
The Rydberg constant equation has two terms that vary depending on the species under consideration, the reduced mass of the electron/nucleus combination and the charge of the nucleus ( Z ).
a. Determine the approximate ratio between the Rydberg constants for isoelectronic He+ (considered the most abundant helium-4 isotope) and H. The masses of the electron, proton, and that of the He+ nucleus (He2+ is a particle ) are given on the inside back cover of this text.
b. Use this ratio to calculate an approximate Rydberg constant ( J ) for He+ .
c. The difference between the He+ 2 s and 1 s orbitals was reported as 329179.76197(20) cm-1 .
Calculate the He+ Rydberg constant from this spectral line for comparison to your value from b. (Data from the same reference as Problem 2.6 .)
풀이:
2.9
The details of several steps in the particle-in-a-box model in this chapter have been omitted. Work out the details of the following steps:
a. Show that if = A sin rx + B cos sx ( A , B , r , and s are constants) is a solution to the wave equation for the one-dimensional box, then
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