An electron is confined to a square well of length L (in picometers). What would be the length of the box such that the energy corresponding to n=2 of the electron is equal to its rest mass energy, mc2 where m is the mass of electron? O 343 3.43 103 O 10.3 O2.92

An electron is confined to a square well of length L (in picometers). What would be the length of the box such that the energy corresponding to n=2 of the electron is equal to its rest mass energy, mc2 where m is the mass of electron? O 343 3.43 103 O 10.3 O2.92

Chemistry: An Atoms First Approach

2nd Edition

ISBN:9781305079243

Author:Steven S. Zumdahl, Susan A. Zumdahl

Publisher:Steven S. Zumdahl, Susan A. Zumdahl

Chapter2: Atomic Structure And Periodicity

Section: Chapter Questions

Problem 66E: Consider an electron for a hydrogen atom in an excited state. The maximum wavelength of...

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Question

An electron is confined to a square well of length L (in picometers). What would be the length of the box such that the energy corresponding to n=2 of the electron is equal to its rest
mass energy, mc2 where m is the mass of electron?
O 343
3.43
103
O 10.3
O2.92

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The wave function for the 2pz, orbital in the hydrogen atom is 2pl=142(za0)3/2e/2cos where a0 is the value for the radius of the first Bohr orbit in meters (5.29 | 1011), is Z(r/a0), r is the value for the distance from the nucleus in meters, and is an angle. Calculate the value of 2pz2 at r = a0 for = 0 (z axis) and for = 90 (xy plane).
(a) Use the radial wave function for the 3p orbital of a hydrogen atom (see Table 5.2) to calculate the value of r for which a node exists. (b) Find the values of r for which nodes exist for the 3s wave function of the hydrogen atom.
For hydrogen atoms, the wave function for the state n = 3, l = 0, ml = 0 is 300=1813(1a0)3/2(2718+22)e where = r/a0 and a0 is the Bohr radius (5.29 1011 m). Calculate the position of the nodes for this wave function.
Consider an electron for a hydrogen atom in an excited state. The maximum wavelength of electromagnetic radiation that can completely remove (ionize) the electron from the H atom is 1460 nm. What is the initial excited state for the electron (n = ?)?
Consider burning ethane gas, C2H6 in oxygen (combustion) forming CO2 and water. (a) How much energy (in J) is produced in the combustion of one molecule of ethane? (b) What is the energy of a photon of ultraviolet light with a wavelength of 12.6 nm? (c) Compare your answers for (a) and (b).
Use the mathematical expression for the 2pz wave function of a one-electron atom (see Table 5.2) to show that the probability of finding an electron in that orbital anywhere in the x-y plane is 0. What are the nodal planes for a dxz orbital and for a dx2y2 orbital?
Investigating Energy Levels Consider the hypothetical atom X that has one electron like the H atom but has different energy levels. The energies of an electron in an X atom are described by the equation E=RHn3 where RH is the same as for hydrogen (2.179 1018 J). Answer the following questions, without calculating energy values. a How would the ground-state energy levels of X and H compare? b Would the energy of an electron in the n = 2 level of H be higher or lower than that of an electron in the n = 2 level of X? Explain your answer. c How do the spacings of the energy levels of X and H compare? d Which would involve the emission of a higher frequency of light, the transition of an electron in an H atom from the n = 5 to the n = 3 level or a similar transition in an X atom? e Which atom, X or H, would require more energy to completely remove its electron? f A photon corresponding to a particular frequency of blue light produces a transition from the n = 2 to the n = 5 level of a hydrogen atom. Could this photon produce the same transition (n = 12 to n = 5) in an atom of X? Explain.

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