c) The Bohr model of the atom postulated electrons orbiting around the nucleus in stableorbits. De Broglie explained what orbits could exist by postulating that electrons (and any-thing else) with momentum p have an associated wavelength λ, given by λ = h/p where his Planck's constant.i)For an electron orbiting around a proton (the Bohr model), equating the centripetalforce with the Coulomb force gives the expression v² = e²/(4πmer). Calculate thespeed of an electron orbiting at the Bohr radius, rB0.053 nm.=ii) Calculate the momenta and the de Broglie wavelengths of the electron of part (i) andof a bird (a racing pigeon) that weighs 0.350 kg and flies at 100 km per hour.iii) Compare the wavelength for the electron that you obtain in (ii) with the circumferenceof the orbit. Comment on this comparison. Explain briefly what it implies about theother possible orbits of the Bohr model and how the higher orbits might be predicted.

Answered: c) The Bohr model of the atom…

Modern Physics

3rd Edition

ISBN:9781111794378

Author:Raymond A. Serway, Clement J. Moses, Curt A. Moyer

Publisher:Raymond A. Serway, Clement J. Moses, Curt A. Moyer

Chapter4: The Particle Nature Of Matter

Section: Chapter Questions

Problem 39P

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(a) What is the momentum of a 0.0100-nm-wavelength photon that could detect details of an atom? (b) What is its energy in MeV?
(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=3 shell?
Atoms can be ionized by thermal collisions, such as at the high temperatures found in the solar corona. One such ion is C+5, a carbon atom with only a single electron. (a) By what factor are the energies of its hydrogen-like levels greater than those of hydrogen? (b) What is the wavelength of the first line in this ion's Paschen series? (c) What type of EM radiation is this?
(a) What is the minimum value of 1 for a subshell that has 11 electrons in it? (b) If this subshell is in the n=5 shell, what is the spectroscopic notation for this atom?
The Balmer series for hydrogen was discovered before either the Lyman or the Paschen series. Why?
(a) Calculate the number of photoelectrons per second ejected from a 1.00-mm2 area of sodium metal by 500-nm M radiation having an intensity of 1.30 kW/m2 (the intensity of sunlight above the Earth's atmosphere). (b) Given that the binding energy is 2.28 eV, what power is carried away by the electrons? (c) The electrons carry away less power than brought in by the photons. Where does the other power go? How can it be recovered?
In extreme-temperature environments, such as those existing in a solar corona, atoms may be ionized by undergoing collisions with other atoms. One example of such ionization in the solar corona is the presence of C5+ ions, detected in the Fraunhofer spectrum. (a) By what factor do the energies of the C5+ ion scale compare to the energy spectrum of a hydrogen atom? (b) What is the wavelength of the first line in the Paschen series of C5+ ? (c) In what part of the spectrum are these lines located?
A Thomson-type experiment with relativistic electrons. One of the earliest experiments to show that p = mv (rather than p = mv) was that of Neumann. [G. Neumann, Ann. Physik 45:529 (1914)]. The apparatus shown in Figure P4.5 is identical to Thomsons except that the source of high-speed electrons is a radioactive radium source and the magnetic field B is arranged to act on the electron over its entire trajectory from source to detector. The combined electric and magnetic fields act as a velocity selector, only passing electrons with speed v, where v = V/Bd (Equation 4.6), while in the region where there is only a magnetic field the electron moves in a circle of radius r, with r given by p = Bre. This latter region (E = 0, B = constant) acts as a momentum selector because electrons with larger momenta have paths with larger radii. (a) Show that the radius of the circle described by the electron is given by r = (l2 + y2)/2y. (b) Typical values for the Neumann experiment were d = 2.51 104 m, B = 0.0177 T, and l = 0.0247 m. For V = 1060 V, y, the most critical value, was measured to be 0.0024 0.0005 m. Show that these values disagree with the y value calculated from p = mv but agree with the y value calculated from p = mv within experimental error. (Hint: Find v from Equation 4.6, use mv = Bre or mv = Bre to find r, and use r to find y.) Figure P4.5 The Neumann apparatus.
(a) If the position of a chlorine ion in a membrane is measured to an accuracy of 1.00 m, what is its minimum uncertainty in velocity, given its mass is 5.8601026 kg? (b) If the ion has this velocity, what is its kinetic energy in eV, and how does this compare with typical molecular binding energies?
A beryllium ion with a single electron (denoted Be3+) is in an excited state with radius the same as that of the ground state of hydrogen. (a) What is n for the Be3+ ion? (b) How much energy in eV is needed to ionize the ion from this excited state?

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