Universe: Stars And Galaxies
6th Edition
ISBN: 9781319115098
Author: Roger Freedman, Robert Geller, William J. Kaufmann
Publisher: W. H. Freeman
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Chapter 5, Problem 40Q
To determine
(a)
If it is possible for a hydrogen atom in the ground state to absorb an H-alpha photon.
To determine
(b)
If it is possible for a hydrogen atom in
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A hypothetical atom has only two atomic energy levels, separated by 3.2 eV. Suppose that at a certain altitude in the atmosphere of a star there are 6.1 * 1013/cm3 of these atoms in the higher-energy state and 2.5 * 1015/cm3 in the lower-energy state. What is the temperature of the star’s atmosphere at that altitude?
A hydrogen atom in an n=2 state absorbs a photon.What wavelength photons might be emitted by the atom following absorption?For your answer: You should find 10 total possible wavelengths, with the shortest being ~100 nm and the largest being ~1900nm. You should enumerate all of them.
The light observed that is emitted by a hydrogen atom is explained by a simple model of its structure with one proton in its nucleus and an electron bound to it, but only with internal energies of the atom satisfying
EH=−RH/n2EH=−RH/n2
where RHRH is the Rydberg constant and nn is an integer such as 1, 2, 3 ... and so on. When a hydrogen atom in an excited state emits light, the photon carries away energy and the atom goes into a lower energy state.
Be careful about units. The Rydberg constant in eV is
13.605693009 eV
That would be multiplied by the charge on the electron 1.602× 10-19 C to give
2.18× 10-18 J
A photon with this energy would have a frequency f such that E=hf. Its wavelength would be λ = c/f = hc/E. Sometimes it is handy to measure the Rydberg constant in units of 1/length for this reason. You may see it given as 109737 cm-1 if you search the web, so be aware that's not joules.
The following questions are intended to help you understand the connection between…
Chapter 5 Solutions
Universe: Stars And Galaxies
Ch. 5 - Prob. 1QCh. 5 - Prob. 2QCh. 5 - Prob. 3QCh. 5 - Prob. 4QCh. 5 - Prob. 5QCh. 5 - Prob. 6QCh. 5 - Prob. 7QCh. 5 - Prob. 8QCh. 5 - Prob. 9QCh. 5 - Prob. 10Q
Ch. 5 - Prob. 11QCh. 5 - Prob. 12QCh. 5 - Prob. 13QCh. 5 - Prob. 14QCh. 5 - Prob. 15QCh. 5 - Prob. 16QCh. 5 - Prob. 17QCh. 5 - Prob. 18QCh. 5 - Prob. 19QCh. 5 - Prob. 20QCh. 5 - Prob. 21QCh. 5 - Prob. 22QCh. 5 - Prob. 23QCh. 5 - Prob. 24QCh. 5 - Prob. 25QCh. 5 - Prob. 26QCh. 5 - Prob. 27QCh. 5 - Prob. 28QCh. 5 - Prob. 29QCh. 5 - Prob. 30QCh. 5 - Prob. 31QCh. 5 - Prob. 32QCh. 5 - Prob. 33QCh. 5 - Prob. 34QCh. 5 - Prob. 35QCh. 5 - Prob. 36QCh. 5 - Prob. 37QCh. 5 - Prob. 38QCh. 5 - Prob. 39QCh. 5 - Prob. 40QCh. 5 - Prob. 41QCh. 5 - Prob. 42QCh. 5 - Prob. 43QCh. 5 - Prob. 44QCh. 5 - Prob. 45QCh. 5 - Prob. 46QCh. 5 - Prob. 47QCh. 5 - Prob. 48QCh. 5 - Prob. 49QCh. 5 - Prob. 50QCh. 5 - Prob. 51Q
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- 4. a. An electron in a hydrogen atom falls from an initial energy level of n-5 to a final level of n - 2. Find the energy, frequency, and wavelength of the photon that will be [For hydrogen: E-13.6 eV/n²] emitted for this sequence. b. A photon of energy 2.794 eV is absorbed by a hydrogen atom, causing its electron to be released with a kinetic energy of 2.250 eV. In what energy level was the electron? c. Find the wavelength of the matter wave associated with a proton moving at a speed of 350 m/s.arrow_forwardQ) A hydrogen atom emits radiation as a result of an electron transition to a lower energy level. Determine the highest frequency possible due to this transition if the atom emits a series of lines that lie in the visible part of the spectrum. Then, if the electron ends up in n = 1 level, prove that the atom emits a series of lines of wavelength that are not in the visible part of the spectrum.arrow_forwardB) A Hydrogen atom initially in its third level, emitted a photon and ends down in its ground state. What must have been the frequency of the photon? Now the electron makes spontaneous absorb and comes back to the third level. What are the possible frequencies of the photons absorbed during this process?arrow_forward
- 1) The Lyman series of lines in the emission spectrum of hydrogen corresponds to transitions from various excited states to the n1 = 1 orbit. Calculate the wavelength (in nm) of the energy line (n = 11) in the Lyman series to five significant figures. (RH = 109677.57 cm-1). Think about where this is in the spectrum. 2) What is the wavelength, (in angstroms, A) of an electron (m = 9.11 X 10-31 kg) moving at 7.80 X 105 m/sec. (h= 6.626 X 10-34 Js)arrow_forwardChapter 39, Problem 052 A hydrogen atom is excited from its ground state to the state with n = 4. (a) How much energy must be absorbed by the atom? Consider the photon energies that can be emitted by the atom as it de-excites to the ground state in the several possible ways. (b) How many different energies are possible; what are the (c) highest, (d) second highest, (e) third highest, (f) lowest, (g) second lowest, and (h) third lowest energies? (a) Number Units (b) Number Units (c) Number Units (d) Number Units (e) Number Units (f) Number Units (g) Number Units (h) Number Unitsarrow_forwardH-alpha line is a red visible spectral line in hydrogen atom with a wavelength of 656.3 nm. Consider five distant stars labeled A, B, C, D, and E. The light from these starts was detected on Earth and, after performing spectral analysis, the following H-alpha wavelengths were measured: A = 665.5 nm, AB = 643.7 nm, Ac = 653.9 nm, Ap = 663 nm, and AE = 661.2 nm. Which star has the slowest speed relative to Earth, in which direction and how fast does it move? ✓ Earth. The slowest star is CV and it moves towards The speed of the slowest star (in km/s), Vslowest Which star has the fastest speed relative to Earth, in which direction and how fast does it move? The fastest star is B ✓ and it moves towards = -1.095E12 X Units km/s The speed of the fastest star (in km/s), Vfastest = -5.73E6 Earth. x Units km/sarrow_forward
- A hydrogen atom has its electron in the n-3 state. How much energy would have to be absorbed by the atom for it to become ionized from this level? What is the frequency of the photon that could produce this result? An atom has 46 electrons. What is the smallest value of n needed so that all 46 electrons occupy the lowest possible quantum states consistent with the Pauli exclusion principle? O 1.51 eV 3.65 x 10^14 Hz, n = 5 O 1.51 eV 3.93 x 10^14 Hz. n=5 O 1.58 eV 3.93 x 10^14 Hz, n=5 1.51 eV 3.65 x 10^14 Hz. n-4 O 144 eV 3.65 x 10^14 Hz, n=6arrow_forwardHydrogen gas can be placed inside a strong magnetic field B=12T. The energy of 1s electron in hydrogen atom is 13.6 eV ( 1eV= 1.6*10 J ). a) What is a wavelength of radiation corresponding to a transition between 2p and 1s levels when magnetic field is zero? b) What is a magnetic moment of the atom with its electron initially in s state and in p state? c) What is the wavelength change for the transition from p- to s- if magnetic field is turned on?arrow_forwardH-alpha line is a red visible spectral line in hydrogen atom with a wavelength of 656.3 nm. Consider five distant stars labeled A, B, C, D, and E. The light from these starts was detected on Earth and, after performing spectral analysis, the following H-alpha wavelengths were measured: AA = 667.5 nm, Ag = 650.4 nm, Ac = 653.5 nm, Ap = 660.3 nm, and AE = 664.9 nm. Which star has the slowest speed relative to Earth, in which direction and how fast does it move? The slowest star is? and it moves Select an answer The speed of the slowest star (in km/s), Vslowest = Which star has the fastest speed relative to Earth, in which direction and how fast does it move? The fastest star is? and it moves Select an answer Earth. The speed of the fastest star (in km/s), Vfastest Submit Question = Earth. Units Select an answer ✓ Units Select an answer ✓arrow_forward
- A Rydberg hydrogen atom is in the n=45 energy state. (a) What is the energy difference (in eV) between this state and the n=46 level (b) What is the ionization energy of the atom in the n=45 level? (c) What are the frequency and wavelength of a photon emitted in the n=46→n=45 transition? (d ) What is the radius of the atom in the n=45 level? How does this compare with the Bohr radius?arrow_forwardA hydrogen atom is in its fourth excited state. The atom emits a 1.28E+3nm wavelength photon. Determine the maximum possible orbital angular momentum of the electron after emission. Express your answer as multiples of hbar.arrow_forward
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