Essential University Physics: Volume 2 (3rd Edition)
3rd Edition
ISBN: 9780321976420
Author: Richard Wolfson
Publisher: PEARSON
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Chapter 34.5, Problem 34.5GI
To determine
De Broglie’s matter wave hypothesis explains the quantization of electron orbits in the Bhor atom most fundamentally in terms of what.
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In Bohr's model for hydrogen-like atoms, prove the assumption that theangular momentum should be quantized ( L = nh n =1,2,3... ) using the Broglie wavelength equation.
De Broglie explained the Bohr model of the hydrogen atom by attributing a wavelength > to
a particle, with the value of λ coming from the momentum p = mv as λ = h/p.
i) Calculate the de Broglie wavelength of a bird (a racing pigeon) that weighs 0.350 kg
and flies at 100 km per hour.
ii) Equating the centripetal force on an electron orbiting around a proton with the Coulomb
force gives the expression v² = e²/(4πomer). Calculate the speed of an electron or-
biting at the Bohr radius, B = 0.053 nm.
iii) Calculate the momentum and the de Broglie wavelength of an electron moving at the
speed you obtain in (ii).
iv) Compare the wavelength you obtain in (iii) with the circumference of the orbit. Com-
ment on this comparison. Explain briefly what it implies about the possible orbits of
the Bohr model and how the higher orbits might be predicted.
The electron in a hydrogen atom is excited from the quantum energy level n = 1 to n = 4. (a) How much
energy is absorbed by the electron? (b) What are the frequency (v) and wavelength (2., in nanometers) of
the photon absorbed by the electron? (c) What is the energy change (AE, in Joule) when this electron
jumps from the quantum energy level n =4 to n= 2? (d) Calculate the wavelength (in nm) of the photon
emitted by this electronic transition. (E, = -(2.18 x 10-18 J)/n²; h= 6.63 x 10-34 J.s; c = 3.00 x 10° m/s)
Chapter 34 Solutions
Essential University Physics: Volume 2 (3rd Edition)
Ch. 34.2 - Prob. 34.1GICh. 34.3 - If you replot Fig. 34.7 for a material with a...Ch. 34.3 - Prob. 34.3GICh. 34.4 - Prob. 34.4GICh. 34.5 - Prob. 34.5GICh. 34.6 - Prob. 34.6GICh. 34 - Prob. 1FTDCh. 34 - Prob. 2FTDCh. 34 - Prob. 3FTDCh. 34 - Prob. 4FTD
Ch. 34 - Prob. 5FTDCh. 34 - Prob. 6FTDCh. 34 - Prob. 7FTDCh. 34 - Prob. 8FTDCh. 34 - Prob. 9FTDCh. 34 - Prob. 10FTDCh. 34 - Prob. 11FTDCh. 34 - Prob. 12FTDCh. 34 - Prob. 13FTDCh. 34 - Prob. 14FTDCh. 34 - Prob. 15ECh. 34 - The surface temperature of the star Rigel is 104K....Ch. 34 - Prob. 17ECh. 34 - Prob. 18ECh. 34 - Prob. 19ECh. 34 - Prob. 20ECh. 34 - Prob. 21ECh. 34 - Prob. 22ECh. 34 - Prob. 23ECh. 34 - Prob. 24ECh. 34 - Prob. 25ECh. 34 - Prob. 26ECh. 34 - Prob. 27ECh. 34 - Prob. 28ECh. 34 - Prob. 29ECh. 34 - Prob. 30ECh. 34 - Prob. 31ECh. 34 - Prob. 32ECh. 34 - Prob. 33ECh. 34 - Prob. 34ECh. 34 - Prob. 35ECh. 34 - Prob. 36ECh. 34 - Prob. 37ECh. 34 - Prob. 38PCh. 34 - Prob. 39PCh. 34 - Prob. 40PCh. 34 - Prob. 41PCh. 34 - Prob. 42PCh. 34 - Prob. 43PCh. 34 - Prob. 44PCh. 34 - Prob. 45PCh. 34 - Prob. 46PCh. 34 - Prob. 47PCh. 34 - Prob. 48PCh. 34 - Prob. 49PCh. 34 - Prob. 50PCh. 34 - Prob. 51PCh. 34 - Prob. 52PCh. 34 - Prob. 53PCh. 34 - Prob. 54PCh. 34 - Prob. 55PCh. 34 - Prob. 56PCh. 34 - Prob. 57PCh. 34 - Prob. 58PCh. 34 - Prob. 59PCh. 34 - Prob. 60PCh. 34 - Prob. 61PCh. 34 - Prob. 62PCh. 34 - Prob. 63PCh. 34 - Prob. 64PCh. 34 - Prob. 65PCh. 34 - Prob. 66PCh. 34 - Prob. 67PCh. 34 - Prob. 68PCh. 34 - Prob. 69PCh. 34 - Prob. 70PCh. 34 - Prob. 71PCh. 34 - Prob. 72PCh. 34 - Prob. 73PCh. 34 - Prob. 74PCh. 34 - Prob. 75PCh. 34 - Prob. 76PCh. 34 - Prob. 77PCh. 34 - Prob. 78PCh. 34 - Prob. 79PCh. 34 - Prob. 80PCh. 34 - Prob. 81PCh. 34 - Prob. 82PCh. 34 - Prob. 83PCh. 34 - Prob. 84PPCh. 34 - Prob. 85PPCh. 34 - Prob. 86PPCh. 34 - Prob. 87PP
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- The Balmer series for hydrogen was discovered before either the Lyman or the Paschen series. Why?arrow_forwardDerive an expression for the ratio of X-ray photon frequency for two elements with atomic numbers Z1 and Z2.arrow_forward(a) Using Bohr’s second postulate of quantization of orbital angular momentum show that the circumference of the electron in the n,h orbital state in hydrogen atom is n times the de-Broglie wavelength associated with it. (b) The electron in hydrogen atom is initially in the third excited state. What is the maximum number of spectral lines which can be emitted when it finally moves to the ground state?arrow_forward
- 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_forwardWe have discovered that an electron’s orbit must contain an integer number of de Broglie wavelengths. Explain why, under ordinary conditions, this makes it impossible for electrons to spiral in to merge with the positively charged nucleus.arrow_forwardSuppose that the uncertainty in position of an electron is equal to the radius of the n=1n=1 Bohr orbit, about 0.529×10−10m0.529×10−10m. A) Calculate the minimum uncertainty in the corresponding momentum component. Express your answer in kilogram meters per second. B) Compare this with the magnitude of the momentum of the electron in the n=1n=1 Bohr orbit. Compare this with the magnitude of the momentum of the electron in the Bohr orbit. a) This is greater than the magnitude of the momentum of the electron in the n=1n=1 Bohr orbit. b) This is the same as the magnitude of the momentum of the electron in the n=1n=1 Bohr orbit. c) This is less than the magnitude of the momentum of the electron in the n=1n=1 Bohr orbit.arrow_forward
- (a) Using de-Broglie’s hypothesis, explain with the help of a suitable diagram, Bohr’s second postulate of quantization of energy levels in a hydrogen atom. (b) The ground state energy of hydrogen atom is -13.6 eV. What are the kinetic and potential energies of the state?arrow_forwardThree energy levels exist in a particular atom (not necessarily hydrogen-like with a single electron [Bohr model doesn’t apply]) such that when an electron transitions from the n=3 energy level to n=2, a photon of wavelength 600 nm is emitted. When an electron transitions from n=3 to n=1 a photon of wavelength 200 nm is emitted. The wavelength of the emitted photon when an electron transitions from n=2 to n=1 is ____ nm.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_forward
- An electron has a de Broglie wavelength equal to the diameter of a hydrogen atom in its ground state. (a) What is the kinetic energy of the electron? (The Bohr radius is 0.0529 nm.) eV(b) How does this energy compare with the magnitude of the ground-state energy of the hydrogen atom? many orders of magnitude smallerabout 10 times as small about the sameabout 10 times as largemany orders of magnitude largerarrow_forwardA Bohr-like atom has a ground state energy (n=1) of -41.4eV. An electron makes a transition from the n=4 state to the n=2 state. The emitted photon is then incident onto a metal surface with a work function equal to 3.34eV. What is the wavelength (nm) of the emitted photon?HINT: Bohr-like atom means that the energy, En, of the n-th level scales as En=E1/n^2, where E1 is the ground state energy.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
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