COLLEGE PHYSICS,V.2
11th Edition
ISBN: 9781305965522
Author: SERWAY
Publisher: CENGAGE L
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Chapter 28, Problem 25P
(a)
To determine
The radius of the orbit.
(b)
To determine
The wavelength of the electron in this orbit.
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An electron is in the second excited orbit of hydrogen, corresponding to n = 3. Find (a) the radius of the orbit and (b) the wavelength of the electron in this orbit.
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Chapter 28 Solutions
COLLEGE PHYSICS,V.2
Ch. 28.3 - Prob. 28.1QQCh. 28.4 - Prob. 28.2QQCh. 28.5 - Prob. 28.3QQCh. 28 - Prob. 1CQCh. 28 - Prob. 2CQCh. 28 - Prob. 3CQCh. 28 - Prob. 4CQCh. 28 - Prob. 5CQCh. 28 - Prob. 6CQCh. 28 - Prob. 7CQ
Ch. 28 - Prob. 8CQCh. 28 - Prob. 9CQCh. 28 - Prob. 10CQCh. 28 - Prob. 11CQCh. 28 - Prob. 12CQCh. 28 - Prob. 13CQCh. 28 - Prob. 14CQCh. 28 - Prob. 15CQCh. 28 - Prob. 1PCh. 28 - Prob. 2PCh. 28 - Prob. 3PCh. 28 - Prob. 4PCh. 28 - Prob. 5PCh. 28 - Prob. 6PCh. 28 - Prob. 7PCh. 28 - Prob. 8PCh. 28 - Prob. 9PCh. 28 - Prob. 10PCh. 28 - Prob. 11PCh. 28 - Prob. 12PCh. 28 - Prob. 13PCh. 28 - Prob. 14PCh. 28 - Prob. 15PCh. 28 - Prob. 16PCh. 28 - Prob. 17PCh. 28 - Prob. 18PCh. 28 - Prob. 19PCh. 28 - Prob. 20PCh. 28 - Prob. 21PCh. 28 - Prob. 22PCh. 28 - Prob. 23PCh. 28 - Prob. 24PCh. 28 - Prob. 25PCh. 28 - Prob. 26PCh. 28 - Prob. 27PCh. 28 - Prob. 28PCh. 28 - Prob. 29PCh. 28 - Prob. 30PCh. 28 - Prob. 31PCh. 28 - Prob. 32PCh. 28 - Prob. 33PCh. 28 - Prob. 34PCh. 28 - Prob. 35PCh. 28 - Prob. 36PCh. 28 - Prob. 37PCh. 28 - Prob. 38PCh. 28 - Prob. 39PCh. 28 - Prob. 40PCh. 28 - Prob. 41PCh. 28 - Prob. 42PCh. 28 - Prob. 43PCh. 28 - Prob. 44PCh. 28 - Prob. 45PCh. 28 - Prob. 46APCh. 28 - Prob. 47APCh. 28 - Prob. 48APCh. 28 - Prob. 49APCh. 28 - Prob. 50APCh. 28 - Prob. 51APCh. 28 - Prob. 52APCh. 28 - Prob. 53APCh. 28 - Prob. 54AP
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- An electron is in the nth Bohr orbit of the hydrogen atom. (a) Show that the period of the electron is T = n3t0 and determine the numerical value of t0. (b) On average, an electron remains in the n = 2 orbit for approximately 10 ms before it jumps down to the n = 1 (ground-state) orbit. How many revolutions does the electron make in the excited state? (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_forwardThe average value (or expected value) of r^k, where r is the distance of an electron in the state with principal quantum number n and orbital quantum number leo proton in the hydrogen atom is given by the integral below, where Pnl(r) is a radial probability density of the state with quantum number n, lek is an arbitrary power. For an electron in the ground state of the hydrogen atom. a) calculate <r>nl in terms of the Bohr radius aB b) calculate <l/r>nl in terms of aB c) calculate <U(r)>nl, where U(r) = -e^2/(4piE0r). Respond in eV units. d) Considering also that the electron is in the ground state, estimate the expected value for two kinetic energy <K> and its mean quadratic velocity v. e) Is it justifiable to disregard relativistic corrections for this system? Justify.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_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_forwardA) By what factor is the uncertainty of the electron's position(1.36×10-4 m) larger than the diameter of the hydrogen atom?(Assume the diameter of the hydrogen atom is 1.00×10-8 cm.) B) Use the Heisenberg uncertainty principle to calculate Δx for a ball (mass = 122 g, diameter = 8.50 cm) with Δv = 0.425 m/s. C) The uncertainty of the (above) ball's position is equal to what factor times the diameter of the ball?arrow_forwardWhat is the orbital radius of the n = 3 excited state in the Bohr model of the hydrogen atom in nanometers? The ground-state radius of the hydrogen atom is 0.529 × 10-10 m. Please give your answer with 3 decimal places.arrow_forward
- (a) A hydrogen atom has its electron in the n = 6 level. The radius of the electron's orbit in the Bohr model is 1.905 nm. Find the de Broglie wavelength of the electron under these circumstances. m (b) What is the momentum, mv, of the electron in its orbit? kg-m/sarrow_forward(a) Using the Bohr model, calculate the speed of the electron in a hydrogen atom in the n = 1, 2, and 3 levels. (b) Calculate the orbital period in each of these levels. (c) The average lifetime of the first excited level of a hydrogen atom is 1.0 * 10-8 s. In the Bohr model, how many orbits does an electron in the n = 2 level complete before returning to the ground level?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
- (a) A hydrogen atom has its electron in the n = 2 level. The radius of the electron's orbit in the Bohr model is 0.212 nm. Find the de Broglie wavelength of the electron under these circumstances. (b) What is the momentum, mv, of the electron in its orbit?arrow_forwardConsidering the Bohr’s model, given that an electron is initially located at the ground state (n=1n=1) and it absorbs energy to jump to a particular energy level (n=nxn=nx). If the difference of the radius between the new energy level and the ground state is rnx−r1=5.247×10−9rnx−r1=5.247×10−9, determine nxnx and calculate how much energy is absorbed by the electron to jump to n=nxn=nx from n=1n=1. A. nx=9nx=9; absorbed energy is 13.4321 eV B. nx=10nx=10; absorbed energy is 13.464 eV C. nx=8nx=8; absorbed energy is 13.3875 eV D. nx=20nx=20; absorbed energy is 13.566 eV E. nx=6nx=6; absorbed energy is 13.22 eV F. nx=2nx=2; absorbed energy is 10.2 eV G. nx=12nx=12; absorbed energy is 13.506 eV H. nx=7nx=7; absorbed energy is 13.322 eVarrow_forwardThe time-independent w (r) = √ 1 P = wavefunction of the ground state of the hydrogen electron is a function of radial position r. y 3/2 elas In the equation, ao 0.0529 nm is the Bohr radius. What is the probability P of finding the hydrogen electron within a spherical shell of inner radius 0.00600 nm and outer radius 0.0316 nm?arrow_forward
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