Schaum's Outline of College Physics, Twelfth Edition (Schaum's Outlines)
12th Edition
ISBN: 9781259587399
Author: Eugene Hecht
Publisher: McGraw-Hill Education
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Chapter 42, Problem 21SP
To determine
To show: ThatPlanck’s constant
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Ex. 20: Find the value of energy of electron in
eV in the third Bohr orbit of hydrogen atom.
(Rydberg's constant (R) = 1.097 × 107 m¹,
Planck's constant (h) = 6.63 × 10-34 J-s, velocity
of light in air (c) = 3 × 108 m/s).
The quantum-mechanical treatment of the hydrogen atomgives the energy, E, of the electron as a function of the principal quantum number, n:E=-h²/8π²mₑ²aₒ²n² (n=123...) where his Planck’s constant, meis the electron mass, and a0 is 52.92X10⁻¹² =-m.(a) Write the expression in the form E(constant)=-(constant)1/n² , evalu-ate the constant (in J), and compare it with the corresponding expression from Bohr’s theory.(b) Use the expression to find ΔE between n=2 and n=3.(c) Calculate the wavelength of the photon that corresponds tothis energy change. Is this photon seen in the hydrogen spectrumobtained from experiment
The quantum state of an electron in an atom is described by quantum numbers n = 6, ℓ = 4, and mℓ = 1. The orbital total angular momentum of the electron is measured to be x × h/2π, where h is Planck’s constant. What is the number x(remember to use the scientific notation)?
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Schaum's Outline of College Physics, Twelfth Edition (Schaum's Outlines)
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- An electron in a particular atom jumps from an orbit where the energy is higher than that of the final lower- energy orbit. What is the magnitude of the energy difference (in eV) of the two energy levels if the emitted photon has a wavelength of 490 nm? [Planck's constant h=4.14 X 10^-15 eV X s]arrow_forwardIn the ground state of hydrogen, the uncer- tainty in the position of the electron is roughly 0.11 nm. The mass of an electron is 9.10939 × 10-31 kg and Planck's constant is 6.62608 × 10 What is the uncertainty of the speed for this electron if the speed has been measured as precisely as possible? Answer in units of m/s. -34 J. s.arrow_forwardEx. 40: Calculate the de Broglie wavelength of proton, if it is moving with speed of 2 x 10 m/s. Mass of proton (m) = 1.67 x 10 " kg. Planck's %3D constant = 6.625 x 10-34 Js. %3Darrow_forward
- An X-ray photon with a wavelength of 0.944 nm strikes a surface. The emitted electron has a kinetic energy of 961 eV . What is the binding energy of the electron in kJ/mol ? [Note that KE=12mv2 and 1 electronvolt (1eV)=1.602×10−19J. (Please type answer no write by hend)arrow_forwardThe quantum state of an electron in an atom is described by quantum numbers n = 6, ℓ = 5, and mℓ = 2. The z-component orbital angular momentum of the electron is measured to be x × h/2π, where h is Planck’s constant. What is the number x (remember to use the scientific notation)?arrow_forward79. a) Assume an electron in the ground state of the hydrogen atom moves at an average speed of 5.00×106 m/s. If the speed is known to an uncertainty of 1 percent, what is the minimum uncertainty in its position?The radius of the hydrogen atom in the ground state is 5.29×10−11 m. The mass of an electron is 9.1094×10−31 kg. (b) A 0.16−kg baseball thrown at 100 mph has a momentum of 7.2 kg·m/s. If the uncertainty in measuring the mass is 1.0×10^−7 of the mass, calculate the uncertainty in the baseball's position.arrow_forward
- The magnitude of the spin angular momentum, in terms of Planck's constant h, for a proton is A. 2.00 h B. 0.069 h O C. 0.138 h D. 0.276 h O E. 0.552 harrow_forwarda. A hydrogen atom has its electron in the n = 4 level. The radius of the electron’s orbit in the Bohr model is 0.847 nm. Find the de Broglie wavelength of the electron under these circumstances. [Answer: 5.32 x 10^‐2 m] b. What is the momentum, mv, of the electron in its orbit? [Answer: 25 x 10‐25 kg/m/s]arrow_forwardA hydrogen atom emits a photon when its electron shifts from a higher energy level to a lower one. Suppose that one atom emits a photon whose wavelength equals 656 nm. If the energy levels are defined by the quantum number n (where n = 1, 2, 3, ), what were the initial and final values of n? ni=. ? nf=. ?arrow_forward
- A quantum of electromagnetic radiation has an energy of 1.02 keV. What is its wavelength? The speed of light is 2.99792 x 10° m/s, and Planck's constant is 6.62607 × 10¬34 J. s. Answer in units of nm.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_forwardLight of frequency 12x1015 Hz shines on to clean caesium metal. What is the maximum kinetic energy of the electrons emitted ? The work function of caesium is 1.5 x 10-19 J and the Planck constant h = 6.63 x 10-34 J s. Round off the answer to 2 decimal places and write answers as power of 10.arrow_forward
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