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A mixture of ordinary hydrogen and tritium, a hydrogen isotope whose nucleus is approximately 3 times more massive than ordinary hydrogen, is excited and its spectrum observed. How far apart in wavelength will the Hα
lines of the two kinds of hydrogen be?
A μ- muon is in the n = 2 state of a muonic atom whose nucleus is a proton. Find the wavelength of the photon emitted when the muonic atom drops to its ground state. In what part of the spectrum is this wavelength?
Show that the frequency of the photon emitted by a hydrogen atom in going from the level n + 1 to the level n is always intermediate between the frequencies of revolution of the electron in the respective orbits.
An excited hydrogen atom emits a photon of wavelength l in returning to the ground state. (a) Derive a formula that gives the quantum number of the initial excited state in terms of l and
R. (b) Use this formula to find ni
for a 102.55-nm photon.
The longest wavelength in the Lyman series is 121.5 nm and the shortest wavelength in the Balmer series is 364.6 nm. Use the figures to find the longest wavelength of light that could ionize hydrogen.
A beam of electrons bombards a sample of hydrogen. Through what potential difference must the electrons have been accelerated if the first line of the Balmer series is to be emitted?
Find the wavelength of the spectral line that corresponds to a transition in hydrogen from the n = 10 state to the ground state. In what part of the spectrum is this?
A proton and an electron, both at rest initially, combine to form a hydrogen atom in the ground state. A single photon is emitted in this process. What is its wavelength?
What effect would you expect the rapid random motion of the atoms of an excited gas to have on the spectral lines they produce?
Find the quantum number that characterizes the earth's orbit around the sun. The earth's mass is 6.0 x 1024 kg, its orbital radius is 1.5 x 1011 m, and its orbital speed is 3.0 x 104 m/s.
