Universe
11th Edition
ISBN: 9781319039448
Author: Robert Geller, Roger Freedman, William J. Kaufmann
Publisher: W. H. Freeman
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Chapter 5, Problem 38Q
(a)
To determine
The wavelength of
(b)
To determine
A schematic diagram of the hydrogen atom and indicate the electron transition, which results in this spectral line.
(c)
To determine
The region of the
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Q) 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.
(A) The electron in a hydrogen atom makes a transition from a higher energy level to the ground level (n = 1). Find the wavelength and frequency of the emitted photon if the higher level is n = 2. (B) Suppose the atom is initially in the higher level corresponding to n = 5. What is the wavelength of the photon emitted when the atom drops from n = 5 to n = 1?(C) What is the radius of the electron orbit for a hydrogen atom for which n = 5? (D) How fast is the electron moving in a hydrogen atom for which n = 5?
(d) A singly ionised helium atom emits light at wavelengths of 230.6nm
and 541nm. Identify the transitions that result in those spectral
lines.
(e) Identify which of the following term symbols are and aren't valid
for states in Hydrogen, stating reasons for your answers. (i) 2s1/2;
(ii) 2s3/2; (iii) 3p1/2; (iv) 3d1/2; (v) 2d5/2.
Chapter 5 Solutions
Universe
Ch. 5 - Prob. 1CCCh. 5 - Prob. 2CCCh. 5 - Prob. 3CCCh. 5 - Prob. 4CCCh. 5 - Prob. 5CCCh. 5 - Prob. 6CCCh. 5 - Prob. 7CCCh. 5 - Prob. 8CCCh. 5 - Prob. 9CCCh. 5 - Prob. 10CC
Ch. 5 - Prob. 11CCCh. 5 - Prob. 12CCCh. 5 - Prob. 13CCCh. 5 - Prob. 14CCCh. 5 - Prob. 1CLCCh. 5 - Prob. 2CLCCh. 5 - Prob. 3CLCCh. 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. 10QCh. 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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- Suppose an electron in a hydrogen atom makes a transition from the (n+1) th orbit to the nth orbit. Is the wavelength of the emitted photon longer for larger values of n, or for smaller values of n?arrow_forwardWhen a hydrogen atom is in its ground state, what are the shortest and longest wavelengths of the photons it can absorb without being ionized?arrow_forwardCalculate the energies and vacuum wavelengths of all possible photons that are emitted when an electron cascades from n=3 to n=1 orbit of the Hydrogen atom. Hint: the answer contains 3 different energies/wavelengths.arrow_forward
- The wave function of a hydrogen atom is in an excited state is: -1/2 W221 = ( m6°)"2 (r/9a) exp(-r/3ao) sin0 cose e“. (a) What is the most probable value of r in this state? How does it relate to the Bohr model prediction for the radius? (b) What is the magnitude of the orbital angular momentum in this state? How does it compare with the Bohr model prediction? (c) Find the orientation of the orbital angular momentum in this state. (d) What is the shortest wavelength photon that the atom can emit making an allowed transition? Identify the terminal state (in Whilm form) and justify why the transition is allowed,arrow_forwardA visible (violet) emission spectral line for chromium (Cr) occurs at wavelength λ = 425.435 nm.What is the frequency (ν) of this light?(Mind the units carefully. Give your answers to six significant figures.)arrow_forwardIf the energy released by an electron making a transition from one hydrogen atom orbit to another is 4.57 ✕ 10−19 J, what is the wavelength (in nm) of the photon?arrow_forward
- a)Suppose a hydrogen molecule in its ground state is dissociated by absorbing a photon of ultraviolet light, causing the two hydrogen atoms to fly apart. What photon energy will give each atom a speed of 19 km/s? The mass of a hydrogen atom is 1.7×10^−27 kg Express your answer to two significant figures and include the appropriate units.arrow_forwardA)Calculate the frequency when an electron drops from n=5 to the n=4 level in a hydrogen atom. Round your answer to 4 significant digits. B)An electron in the hydrogen atom makes a transition from an energy state of principal quantum number ni to the n=2 state. If the photon emitted has a wavelength of 434nm, what is the value of ni? Round your answer to the nearest whole number.)arrow_forwardA hydrogen atom is in its ground state (n; = 1) when a photon impinges upon it. The atom absorbs the photon, which has precisely the energy required to raise the atom to the n, = 3 state. (a) What was the photon's energy (in eV)? ev (b) Later, the atom returns to the ground state, emitting one or more photons in the process. Which of the following energies describes photons that might be emitted thus? (Select all that apply.) O 13.6 eV 1.89 eV 12.1 ev O 10.2 eVarrow_forward
- Calculate the wavelength, in nanometers, of the photon emitted when the electron in a hydrogen atom transitions from the level n1 = 8 to level n2 = 2. Use three significant figures in your answer.arrow_forward) a) What temperature is required for a black body spectrum to peak in the X-ray band? (Assume that E = 1 keV). What is the frequency and wavelength of a 1 keV photon? b) What is one example of an astrophysical phenomenon that emits black body radiation that peaks near 1 keV? c) What temperature is required for a black body spectrum to peak in the gamma-ray band with E = 1 GeV? What is the frequency and wavelength of a 1 GeV photon? d) What is one example of an astrophysical phenomenon that emits black body radiation that peaks at 1 GeV?arrow_forwardThe wavelength of the Lyman alpha emission line of Hydrogen (which we will obtain rather accurately in the Bohr model of the atom) is 121.6nm . In the Lorentz model of the atom, what spring constant does that resonance line correspond to? Please respond in N/m Previous answer give was wrong.arrow_forward
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