EBK PHYSICS
5th Edition
ISBN: 8220103026918
Author: Walker
Publisher: PEARSON
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Chapter 31, Problem 38PCE
To determine
The expression for the de-Broglie wavelength of an electron in the
n th n
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Find an expression, in termsof n and the fundamental constants, for the de Broglie wavelength of an electron in the nthstate of the hydrogen atom
(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?
When a hydrogen atom undergoes a transition from n=3 to n=2 level, a photon with λ=656.5 nm is emitted. (a) If we imagine the atom as an electron in a one-dimensional box, what is the width of the box so that the transition from n=3 to n=2 corresponds to the emission of a photon of this wavelength? (b) For a box with the width calculated in (a), what is the ground energy state? (c) Do you think a one-dimensional box is a good model for a hydrogen atom? Because?
Chapter 31 Solutions
EBK PHYSICS
Ch. 31.1 - Prob. 1EYUCh. 31.2 - Prob. 2EYUCh. 31.3 - Prob. 3EYUCh. 31.4 - Prob. 4EYUCh. 31.5 - Prob. 5EYUCh. 31.6 - Prob. 6EYUCh. 31.7 - Prob. 7EYUCh. 31 - Prob. 1CQCh. 31 - Prob. 2CQCh. 31 - Prob. 3CQ
Ch. 31 - Prob. 4CQCh. 31 - Prob. 5CQCh. 31 - Prob. 6CQCh. 31 - Prob. 7CQCh. 31 - Prob. 8CQCh. 31 - Prob. 9CQCh. 31 - Prob. 1PCECh. 31 - Prob. 2PCECh. 31 - Prob. 3PCECh. 31 - Prob. 4PCECh. 31 - Prob. 5PCECh. 31 - Prob. 6PCECh. 31 - Prob. 7PCECh. 31 - Prob. 8PCECh. 31 - Prob. 9PCECh. 31 - Prob. 10PCECh. 31 - Prob. 11PCECh. 31 - Prob. 12PCECh. 31 - Prob. 13PCECh. 31 - Prob. 14PCECh. 31 - Prob. 15PCECh. 31 - Prob. 16PCECh. 31 - Prob. 17PCECh. 31 - Prob. 18PCECh. 31 - Prob. 19PCECh. 31 - Prob. 20PCECh. 31 - Prob. 21PCECh. 31 - Prob. 22PCECh. 31 - Prob. 23PCECh. 31 - Prob. 24PCECh. 31 - Prob. 25PCECh. 31 - Prob. 26PCECh. 31 - Prob. 27PCECh. 31 - Prob. 28PCECh. 31 - Prob. 29PCECh. 31 - Prob. 30PCECh. 31 - Prob. 31PCECh. 31 - Prob. 32PCECh. 31 - Prob. 33PCECh. 31 - Prob. 34PCECh. 31 - Prob. 35PCECh. 31 - Prob. 36PCECh. 31 - Prob. 37PCECh. 31 - Prob. 38PCECh. 31 - Prob. 39PCECh. 31 - Prob. 40PCECh. 31 - Prob. 41PCECh. 31 - Prob. 42PCECh. 31 - Prob. 43PCECh. 31 - Prob. 44PCECh. 31 - Prob. 45PCECh. 31 - Prob. 46PCECh. 31 - Prob. 47PCECh. 31 - Prob. 48PCECh. 31 - Prob. 49PCECh. 31 - Prob. 50PCECh. 31 - Prob. 51PCECh. 31 - Prob. 52PCECh. 31 - Give the electronic configuration for the ground...Ch. 31 - Prob. 54PCECh. 31 - Prob. 55PCECh. 31 - Prob. 56PCECh. 31 - The configuration of the outer electrons in Ni is...Ch. 31 - Prob. 58PCECh. 31 - Prob. 59PCECh. 31 - Prob. 60PCECh. 31 - Prob. 61PCECh. 31 - Prob. 62PCECh. 31 - Prob. 63PCECh. 31 - Prob. 64PCECh. 31 - Prob. 65PCECh. 31 - Prob. 66PCECh. 31 - Prob. 67PCECh. 31 - Prob. 68GPCh. 31 - Prob. 69GPCh. 31 - Prob. 70GPCh. 31 - Prob. 71GPCh. 31 - Prob. 72GPCh. 31 - Prob. 73GPCh. 31 - Prob. 74GPCh. 31 - Prob. 75GPCh. 31 - Prob. 76GPCh. 31 - Prob. 77GPCh. 31 - Prob. 78GPCh. 31 - Prob. 79GPCh. 31 - Prob. 80GPCh. 31 - Prob. 81GPCh. 31 - Prob. 82GPCh. 31 - Prob. 83GPCh. 31 - Prob. 84PPCh. 31 - Prob. 85PPCh. 31 - Prob. 86PPCh. 31 - Prob. 87PPCh. 31 - Prob. 88PPCh. 31 - Prob. 89PP
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- Calculate the classical mean kinetic energy for the electrons in sodium at room temperature. From this, determine their de Broglie wavelength 2. For a classical description to be valid, we must require that λ is much smaller than the mean separation d of the particles. Show that this is not the case, given that the electron density in sodium is 2.65x1028 m³.arrow_forwardThe total probability of finding an electron in the hydrogen atom is related to the integral ∫ r2 e-2r/ao dr Where r is the distance of the electron from the nucleus and ao is the Bohr radius. Evaluate thisintegral.arrow_forwardCompute the intrinsic line-width (Δλ) of the Lyman α line (corresponding to the n=2 to n=1) transition for the Hydrogen atom. You may assume that the electron remains in the excited state for a time of the order of 10^−8s. The line-width may be computed using:ΔE=(hc/λ^2)Δλarrow_forward
- Compute the oscillation frequency of the electron and the expected absorption or emission wavelength in a Thomson- model hydrogen atom. Use R = 0.053 nm.arrow_forwardA) Calculate the de Broglie wavelength of a neutron (mn = 1.67493×10-27 kg) moving at one six hundredth of the speed of light (c/600). Enter at least 4 significant figures. (I got the answer 949.4 pm but it is wrong, please help) B) Calculate the velocity of an electron (me = 9.10939×10-31 kg) having a de Broglie wavelength of 230.1 pm.arrow_forwardAn electron has energy E = 4?₀ in the regions where it has a potential as shown in the figure below. Considering the regions x > L (region 1) and 0 < x < L (region 2). What will be the ratio between the Broglie wavelengths of the electron in regions 1 and 2, that is, λ₁/λ₂ ?The potential energy is zero within the range 0<x<L and has a constant value Uo outside it.arrow_forward
- What is the de Broglie wavelength for an electron with speed (a) v = 0.480c and (b) v = 0.960c?arrow_forwardFind the typical de Broglie wavelength associated with a He atom in helium gas at room temperature (27 °C) and 1 atm pressure; and compare it with the mean separation between two atoms under these conditions.arrow_forwarda) Calculate the energy of the emissive transition with the lowest energy possible for the Lyman series, for a mole of hydrogen atoms. Express your answer in joules/mol. b) Is this transition in the visible spectral domain? If not, in which region is it located?arrow_forward
- The root mean square speed of the hydrogen molecules at temperature t °C is given by 3x8.31 x (t+273) m 2 x 10-3 Calculate the de Broglie wavelength (in nanometers) of the hydrogen molecules at temperature 24 °C. The mass of the hydrogen molecule is 2 x 1.66 x 10-27 kg. Use two decimals in your answer.arrow_forwardConsider a balloon filled with helium gas at room temperature and atmospheric pressure. Calculate (a) the average de Broglie wavelength of the helium atoms and (b) the average distance between atoms under these conditions. The average kinetic energy of an atom is equal to (3/2)kT, where k is the Boltzmann constant. (c) Can the atoms be treated as particles under these conditions? Explain.arrow_forwardWhat is the de Broglie wavelength (in nanometers!) of an electron with energy 1.2 eV?arrow_forward
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