Modern Physics for Scientists and Engineers
4th Edition
ISBN: 9781133103721
Author: Stephen T. Thornton, Andrew Rex
Publisher: Cengage Learning
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Question
Chapter 4, Problem 34P
(a)
To determine
The difference in the various Bohr radii
(b)
To determine
The difference in the various Bohr radii
(c)
To determine
The difference in the various Bohr radii
(d)
To determine
Show that for Rydberg atoms (hydrogen atoms with large n) the difference between successive radii is approximately
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Students have asked these similar questions
If, 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.
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…
Hydrogen 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?
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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Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, physics and related others by exploring similar questions and additional content below.Similar questions
- (a) If one subshell of an atom has nine electrons in it, what is the minimum value of (b) What is the spectroscopic notation for this atom, if this subshell is part of the n = 3 shell?arrow_forwardIn extreme-temperature environments, such as those existing in a solar corona, atoms may be ionized by undergoing collisions with other atoms. One example of such ionization in the solar corona is the presence of C5+ ions, detected in the Fraunhofer spectrum. (a) By what factor do the energies of the C5+ ion scale compare to the energy spectrum of a hydrogen atom? (b) What is the wavelength of the first line in the Paschen series of C5+ ? (c) In what part of the spectrum are these lines located?arrow_forwardDo the Balmer series and the Lyman series overlap? Why? Why not? (Hint: calculate the shortest Balmer line and the longest Lyman line.)arrow_forward
- a) An electron in a hydrogen atom has energy E= -3.40 eV, where the zero of energy is at the ionization threshold. In the Bohr model, what is the angular momentum of the electron? Express your result as a multiple of ħ. Ans. b) What is the deBroglie wavelength of the electron when it is in this state? Ans. c) When the electron is in this state, what is the ratio of the circumference of the orbit of the electron to the deBroglie wavelength of the electron? Ans. d) The electron makes a transition from the state with energy E= -3.40 eV to the ground state, that has energy -13.6 eV. What is the wavelength of the photon emitted during this transition? Ans.arrow_forwardCompare the Balmer series of hydrogen with the series where n ℓ= 4 for the ionized helium atom He+. What is the difference between the wavelengths of the L ∝ and Lℓ line of hydrogen and the nu = 6 and 8 of He+? Is there a wavelength of the Balmer series that is very similar to any wavelength values where n ℓ = 4 in He+? Explain.arrow_forwardIt is possible that a muon be captured by a proton to form a muonic atom. A muon is identic to an electron, except when your mass, which is m = 105.7 MeV/c^2. What ia the smallest wave length for a Lyman series for this atom? Give your answer in pm.arrow_forward
- A hydrogen atom in an n=2 state absorbs a photon.What wavelength photons might be emitted by the atom following absorption?For the 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.arrow_forwardThe energy difference between the 1st excited state (n = 2) and the 2nd excited state (n = 3) in the hydrogen atom is 1.9 eV, what is the wavelength of the emission line resulting from the electron transitions between those two levels? Give your answer in units of nanometers (nm).arrow_forwardwhere ?∞ = 1.097 × 10^7 m−1is the Rydberg constant and ? is the atomic number (thenumber of protons found in the nucleus). Calculate the ground state energy of a triplyionised beryllium atom, Be3+ (a beryllium atom with three electrons removed).arrow_forward
- A 2.55 eV photon is emitted from a hydrogen atom. What are the Balmer formula n and m values corresponding to this emission?arrow_forwardAn electron is in the nth Bohr orbit of the hydrogen atom. n3 (a) Show that the period of the electron is T = to n³ and determine the numerical value of to. 153 as (b) On average, an electron remains in the n = 2 orbit for approximately 8 us before it jumps down to the n = 1 (ground-state)orbit. How many revolutions does the electron make in the excited state? 8.26e+09 × (c) Define the period of one revolution as an electron year, analogous to an Earth year being the period of the Earth's motion around the Sun. Explain whether we should think of the electron in the n = 2 orbit as "living for a long time."arrow_forwardThree isotopes of hydrogen occur in nature; ordinary hydrogen, deuterium, and tritium. Their nuclei consist of, respectively, 1 proton, 1 proton and 1 neutron (deuteron), and 1 proton and 2 neutrons (triton). (a) Determine Rydberg constants for deuterium and tritium. (b) Determine the wavelength difference between the Balmer α lines of deuterium and tritium. (c) Determine the wavelength difference between the Balmer α lines of hydrogen and tritium. Note: The difference in this case would be caused by the nuclear mass. In deriving the Bohr atom, the first order of approximation was to assume that the nucleus doesn't move at all. The correction to this can be done by replacing the mass of the electron with the reduced mass of the electron-nucleus system, where, as you studied in mechanics, the reduced mass is given by μ=m1m2/(m1+m2). Additionally, the Balmer series is the one that terminates in the n=2 level with the α line corresponding to the n=3→n=2 transition.arrow_forward
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