Modern Physics
3rd Edition
ISBN: 9781111794378
Author: Raymond A. Serway, Clement J. Moses, Curt A. Moyer
Publisher: Cengage Learning
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Question
Chapter 4, Problem 44P
(a)
To determine
The ion in the hot star.
(b)
To determine
The wavelengths of the three spectral lines nearest to the line of the longest wavelength.
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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.
Electrons in multielectron atoms absorb X-rays at characteristic energies, leading to ionization. The characteristic energies for each element allow scientists to identify the element. For magnesium, X-rays with λ = 952 pm are required to selectively eject an electron from the n = 1 energy level, and X-rays with λ = 197 nm remove an electron from the n = 2 energy level.
Calculate the frequency and energy of those X-rays.
Why are the wavelengths and energies different for the two electrons.
Chapter 4 Solutions
Modern Physics
Ch. 4.2 - Exercise 1 Find the horizontal speed vx for this...Ch. 4.2 - Prob. 2ECh. 4.3 - Prob. 3ECh. 4.3 - Prob. 4ECh. 4.3 - Prob. 5ECh. 4 - Prob. 1QCh. 4 - Prob. 2QCh. 4 - Prob. 3QCh. 4 - Prob. 4QCh. 4 - Prob. 5Q
Ch. 4 - Prob. 6QCh. 4 - Prob. 7QCh. 4 - Prob. 8QCh. 4 - Prob. 9QCh. 4 - Prob. 10QCh. 4 - Prob. 11QCh. 4 - Prob. 1PCh. 4 - Prob. 2PCh. 4 - A mystery particle enters the region between the...Ch. 4 - Prob. 4PCh. 4 - A Thomson-type experiment with relativistic...Ch. 4 - Prob. 6PCh. 4 - Prob. 8PCh. 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. 44P
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- The wavelengths of the Brackett series for hydrogen are given by n = 5, 6, 7,.... (a) What are the wavelengths of the first three spectral emission lines in this series (in nm)? (Enter them in order of decreasing wavelength.) largest value nm nm smallest value nm (b) In which band of the electromagnetic spectrum do these lines appear? visible light region O infrared region O ultraviolet region O gamma ray region O x-ray regionarrow_forwardThe Bohr model of the single-electron, many-proton ion predicts the emitted/absorbed photon wavelength for an electron transition between the n,and n2 energy levels is = where R. = 1.097 × 107 m¬1 is the Rydberg constant and Z is the atomic number (the number of protons found in the nucleus). Calculate the ground state energy of a triply ionised beryllium atom, Be3+ (a beryllium atom with three electrons removed).arrow_forward(a) If one subshell of an atom has 9 electrons in it, what is the minimum value of l ? (b) What is the spectroscopic notation for this atom, if this subshell is part of the n = 3shell?arrow_forward
- An 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_forwardA positronium atom consists of a positron and an electron. In a Bohr-like model, the two particles rotate in circles about their common center of mass. (a) Calculate the reduced mass of a positronium atom in terms of the mass of an electron. (b) Determine the orbital radius of its ground-state electron. (c) Find its ground-state energy. (d) The longest visible-light emission wavelength for ordinary hydrogen is 656.3 nm in air and is for the n = 3 to n = 2 transition. Calculate the wavelength for the same transition in positronium.arrow_forwardThe wavelengths of the Lyman series for hydrogen are given by = RH(1-2), = 2, 3, 4, ... 1/2 (a) Calculate the wavelengths of the first three lines in this series. nm nm nm (b) Identify the region of the electromagnetic spectrum in which these lines appear. O ultraviolet region O infrared region O x-ray region O visible light region O gamma ray regionarrow_forward
- In the Bohr model, what is the principal quantum number n at which the excited electron is at a radius of 1 mm?arrow_forwardAn photon with wavelength 3.38 nm is emitted when an electron in a one-electron ion transitions from the first excited state to the ground state. Another emission line, for the same ion is observed at 11.401 nm. It is known that the final energy state in this transition is 2, what is the initial energy state?arrow_forward3:09 O O O 63° A X • N N O 5G „ll Quizzes a (absorption) Brackett series Paschen series Lyman series (emission) Balmer series Paschen series (emission) n= 2 n=3 n=4 .... Lyman series n-5 (a) (b) e These pictures refer to the energy levels of a hydrogen atom. You can find the error in both parts, (a) and (b). The arrows labeled "emission" in (a), and all the arrows in (b), indicate a transition in which an electron jumps from a higher- energy state to a lower-energy state. The different "series" of emission lines are characterized by the index n of the low- energy state in which the electron ends up. In particular, the Lyman series consists of all transitions that end up in the n=1 energy level, with an initial energy level that corresponds to the label n = 2, 3, 4, 5, etc. One of these values of n is not shown as an arrow in the Lyman emission series in figures (a) or (b). This is a significant error because that particular spectral line is very important in astronomy. Pick the value…arrow_forward
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