Modern Physics
3rd Edition
ISBN: 9781111794378
Author: Raymond A. Serway, Clement J. Moses, Curt A. Moyer
Publisher: Cengage Learning
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Chapter 8, Problem 19P
To determine
To prove that the
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Chapter 8 Solutions
Modern Physics
Ch. 8.1 - Prob. 1ECh. 8.1 - Prob. 2ECh. 8.3 - Prob. 3ECh. 8.5 - Prob. 4ECh. 8 - Prob. 1QCh. 8 - Prob. 2QCh. 8 - Prob. 3QCh. 8 - Prob. 4QCh. 8 - Prob. 5QCh. 8 - Prob. 6Q
Ch. 8 - Prob. 1PCh. 8 - Prob. 2PCh. 8 - Prob. 3PCh. 8 - Prob. 4PCh. 8 - Prob. 5PCh. 8 - Prob. 7PCh. 8 - Prob. 8PCh. 8 - Prob. 9PCh. 8 - Prob. 10PCh. 8 - Prob. 11PCh. 8 - Prob. 12PCh. 8 - Prob. 13PCh. 8 - Prob. 14PCh. 8 - Prob. 15PCh. 8 - Prob. 16PCh. 8 - Prob. 17PCh. 8 - Prob. 18PCh. 8 - Prob. 19PCh. 8 - Prob. 20PCh. 8 - Prob. 21PCh. 8 - Prob. 22PCh. 8 - Prob. 23PCh. 8 - Prob. 24PCh. 8 - Prob. 25PCh. 8 - Prob. 26PCh. 8 - Prob. 29PCh. 8 - Prob. 30PCh. 8 - Prob. 31PCh. 8 - Prob. 34P
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- b) One of the n = 5 terms of hydrogen is split by spin-orbit coupling into two levels with an energy difference of 0.0039 cm ¹. Determine the orbital angular momentum quantum number, I, for this state and predict the analogous splitting in Li2+. The fine structure constant, a = 0.0072973.arrow_forwardProve that the degeneracy of an atomic hydrogen state having principal quantum number n is n2. (Ignore the spin quantum number)arrow_forwardThe nuclie 74W ¹42 has first excited state 2* at energy 0.1 Me V above the ground state. Estimate the energies of the lowest lying 4* and 6* rotational states of this nucleus.arrow_forward
- Use all four quantum numbers (n ,ℓ,,mℓ,ms) to write down all possible sets of quantum numbers for the 5d state of atomic hydrogen. What is the total degeneracy?arrow_forwardWhat is the smallest value that ℓ may have if L is within 10° of the z axis?arrow_forwardA hydrogen atom undergoes a transition from a 2p state to the 1s ground state. In the absence of a magnetic field, the wavelength of the photon emitted is 122 nm. The atom is then placed in a strong magnetic field in the z@direction. Ignore spin effects; consider only the interaction of the magnetic field with the atom’s orbital magnetic moment. (a) How many different photon wavelengths are observed for the 2p S 1s transition? What are the ml values for the initial and final states for the transition that leads to each photon wavelength? (b) One observed wavelength is exactly the same with the magnetic field as without. What are the initial and final ml values for the transition that produces a photon of this wavelength? (c) One observed wavelength with the field is longer than the wavelength without the field. What are the initial and final ml values for the transition that produces a photon of this wavelength? (d) Repeat part (c) for the wavelength that is shorter than the wavelength…arrow_forward
- Form factor of atomic hydrogen. For the hydrogen atom in its ground state, the number density is n(r) = (ra)¯ exp(-2r/a), where a, is the Bohr radius. Show that the form factor is fc = 16/(4 + G*a)*. %3Darrow_forward= Using the formula for the hydrogen atom energy levels, En constant can be written in terms of fundamental quantities, RH = Me 4 8€ ²h³c Me4 1 860²h² n²¹ the Rydberg and its value approaches, RH → R = 10,973,731.6 m¹ in the limit μ→ me. (a) How would this constant be defined for a one-electron species containing Z protons in its nucleus? Consider how this changes the form of the Hamiltonian and the energy levels for that Hamiltonian. (b) The hydrogen atom emission lines in the Balmer series (n₂ = 2) lie in the visible portion of the electromagnetic spectrum. Would this also be true if Z> 1? Find the wavelength (in nm) of the n = 32 emission in hydrogen and that for a one-electron species with Z = 2. (You will be asked to report a quantity on the quiz that depends on these two values.)arrow_forwardMeasurements made on the line spectrum emitted by a certain atom of intermediate Z show that the ratio of the separation energies between three adjacent levels of increasing energy in a particular multiplet is approximately 3 to 5 (that is the energy difference between the second and the third member of the multiplet is 5/3 of the energy difference between the first and the second member of the multiplet.) a) What are the j' quantum number that can be assigned to these states? b) What is the l' quantum number that can be assigned to these states? c) What is the s' quantum number that can be assigned to these states?arrow_forward
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