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 33P
(a)
To determine
The Bohr radius of the positronium atom described in the previous problem.
(b)
To determine
The wavelength for the transition from
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(a) Show that the speed of an electron in the nth Bohr orbit of hydrogen is αc/n, where α is the fine structure constant, equal to e2/4πε0ħc. (b) What would be the speed in a hydrogen like atom with a nuclear charge of Ze?
Chapter 4 Solutions
Modern Physics for Scientists and Engineers
Ch. 4 - Prob. 1QCh. 4 - Prob. 2QCh. 4 - Prob. 3QCh. 4 - Prob. 4QCh. 4 - Prob. 5QCh. 4 - Prob. 6QCh. 4 - Prob. 7QCh. 4 - Prob. 8QCh. 4 - Prob. 9QCh. 4 - Prob. 10Q
Ch. 4 - Prob. 11QCh. 4 - Prob. 12QCh. 4 - Prob. 13QCh. 4 - Prob. 2PCh. 4 - Prob. 3PCh. 4 - Prob. 4PCh. 4 - Prob. 5PCh. 4 - Prob. 6PCh. 4 - Prob. 7PCh. 4 - What fraction of 5-MeV α particles will be...Ch. 4 - Prob. 9PCh. 4 - Prob. 10PCh. 4 - Prob. 11PCh. 4 - Prob. 12PCh. 4 - Prob. 13PCh. 4 - Prob. 14PCh. 4 - Prob. 15PCh. 4 - Prob. 16PCh. 4 - Prob. 17PCh. 4 - Prob. 18PCh. 4 - Prob. 19PCh. 4 - Prob. 20PCh. 4 - Prob. 21PCh. 4 - Prob. 22PCh. 4 - Prob. 23PCh. 4 - Prob. 24PCh. 4 - Prob. 25PCh. 4 - Prob. 26PCh. 4 - Prob. 27PCh. 4 - Prob. 28PCh. 4 - Prob. 29PCh. 4 - Prob. 30PCh. 4 - Prob. 31PCh. 4 - Prob. 32PCh. 4 - Prob. 33PCh. 4 - Prob. 34PCh. 4 - Prob. 35PCh. 4 - Prob. 36PCh. 4 - Prob. 37PCh. 4 - Prob. 38PCh. 4 - Prob. 39PCh. 4 - Prob. 40PCh. 4 - Prob. 41PCh. 4 - Prob. 42PCh. 4 - Prob. 43PCh. 4 - Prob. 44PCh. 4 - Prob. 45PCh. 4 - Prob. 46PCh. 4 - Prob. 47PCh. 4 - Prob. 48PCh. 4 - Prob. 49PCh. 4 - Prob. 50PCh. 4 - Prob. 51PCh. 4 - Prob. 52PCh. 4 - Prob. 54PCh. 4 - Prob. 55PCh. 4 - Prob. 56PCh. 4 - Prob. 57PCh. 4 - Prob. 59PCh. 4 - Prob. 60PCh. 4 - Prob. 61P
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- The energy of the n = 2 Bohr orbit is -30.6 eV for an unidentified ionized atom in which only one electron moves about the nucleus. What is the radius of the n = 3 orbit for this species? Number i Units >arrow_forwardA sodium atom (Z = 11) contains 11 protons in its nucleus. Strictly speaking, the Bohr model does not apply, because the neutral atom contains 11 electrons instead of a single electron. However, we can apply the model to the outermost electron as an approximation, provided that we use an effective value Zeffective rather than 11 for the number of protons in the nucleus. (a) The ionization energy for the outermost electron in a sodium atom is 5.1 eV. Use the Bohr model with Z = Zeffective to calculate a value for Zeffective. (b) Using Z = 11, determine the corresponding value for the radius r of the outermost Bohr orbit. (c) Using the value calculated for Zeffective in part (a), determine the corresponding radius r of the outermost Bohr orbit. (a) Zeffective = Number i 2.04 (b) _r= (c)_r= Number i 5.29E-11 Number i 2.12E-11 Units No units Units m Units m ♥arrow_forwardA sodium atom (Z = 11) contains 11 protons in its nucleus. Strictly speaking, the Bohr model does not apply, because the neutral atom contains 11 electrons instead of a single electron. However, we can apply the model to the outermost electron as an approximation, provided that we use an effective value Zeffective rather than 11 for the number of protons in the nucleus. (a) The ionization energy for the outermost electron in a sodium atom is 5.1 eV. Use the Bohr model with Z = Zeffective to calculate a value for Zeffective. (b) Using Z = 11, determine the corresponding value for the radius r of the outermost Bohr orbit. (c) Using the value calculated for Zeffective in part (a), determine the corresponding radius r of the outermost Bohr orbit. (a) Zeffective (b) r = (c) r= Number i Number i Number i Units Units Unitsarrow_forward
- Estimate the energy of the characteristic x-ray emitted from a tungsten target when an electron drops from an M shell (n = 3 state) to a vacancy in the K shell (n = 1 state). The atomic number for tungsten is Z = 74.arrow_forwardA sodium atom (Z = 11) contains 11 protons in its nucleus. Strictly speaking, the Bohr model does not apply, because the neutral atom contains 11 electrons instead of a single electron. However, we can apply the model to the outermost electron as an approximation, provided that we use an effective value Zeffective rather than 11 for the number of protons in the nucleus. (a) The ionization energy for the outermost electron in a sodium atom is 5.1 eV. Use the Bohr model with Z = Zeffective to calculate a value for Zeffective. (b) Using Z = 11, determine the corresponding value for the radius r of the outermost Bohr orbit. (c) Using the value calculated for Zeffective in part (a), determine the corresponding radius r of the outermost Bohr orbit. (a) Zeffective = Number i (b)_r= (c)_r= Number i Number i Units Units Unitsarrow_forwardUse the Bohr theory to estimate the wavelength for an n = 3 to n = 1 transition in molybdenum. The measured value is 0.063 nm. Why do we not expect perfect agreement?arrow_forward
- (a)Calculate the radius (in m) of the orbit for the innermost electron in osmium assuming it is relatively unaffected by the atom's other electrons. Answer in m (b)What is the ratio of this orbital radius to the 6.90 fm radius of the osmium nucleus? answer in relectron Inucleus answer in R electron/R nucluesarrow_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_forwardLook up the values of the quantities in aB = h2 / 4π2 me kqe2 ,and verify that the Bohr radius aB is 0.529 x 10-10 m .arrow_forward
- (a) Find the radius of the n = 4 Bohr orbit of adoubly ionized lithium atom 1Li2+, Z = 32. (b) Is the energy requiredto raise an electron from the n = 4 state to the n = 5 state in Li2+greater than, less than, or equal to the energy required to raise an electron in hydrogen from the n = 4 state to the n = 5 state? Explain.(c) Verify your answer to part (b) by calculating the relevant energies.arrow_forwardIf, in 1 1 = Ry - you set ni = 1 and take n2 greater than 1, you generate what is known as the Lyman %3D series. Find the wavelength of the first mem- ber of this series. The value of ħ is 1.05457 × 10¬34 J.s; the Rydberg constant for hydrogen is 1.09735 × 10’ m¬'; the Bohr radius is 5.29177 × 10¬1" m; and the ground state energy for hydrogen is 13.6057 eV. Answer in units of nm. Consider the next three members of this se- ries. The wavelengths of successive members of the Lyman series approach a common limit as n2 → ∞. What is this limit? Answer in units of nm.arrow_forwardFind the radius and velocity of the electron in n=3 level in hydrogen atom .arrow_forward
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