note that a probability map is not the same as a balloon modelis a probability map of a single s orbital in cross-sectionis a probability map of a single p orbital in cross-section(a)(b)(c)(d)

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Organic Chemistry: A Guided Inquiry

2nd Edition

ISBN:9780618974122

Author:Andrei Straumanis

Publisher:Andrei Straumanis

Chapter3: Electron Orbitals

Section: Chapter Questions

Problem 1CTQ

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How is the Bohr theory of the hydrogen atom inconsistent with the uncertainty principle? In fact, it was this inconsistency, along with the theorys limited application to non-hydrogen-like systems, that limited Bohrs theory.
What experimental evidence supports the quantum theory of light? Explain the wave-particle duality of all matter .. For what size particles must one consider both the wave and the particle properties?
How many nodal planes exist for a 5d orbital? (a) 0 (b) 1 (c) 2 (d) 3
Compare the mass of the electron, me, with a the reduced mass of a hydrogen atom; b the reduced mass of a deuterium atom (deuterium=2H); c the reduced mass of a carbon 12 atom having a +5 charge, that is, C5+. Suggest a conclusion to the trend presented by parts a-c.
Why is the electron in a Bohr hydrogen atom bound less tightly when it has a quantum number of 3 than when it has a quantum number of 1?
Based on the trend shown in Figure 11.5, draw the probability distribution of a harmonic oscillator wavefunction that has a very high value of n. Explain how this is consistent with the correspondence principle.
6.32 What are the mathematical origins of quantum numbers?
(a) The nitrogen atom has one electron in each of the 2px , 2py , and 2pz orbitals. By using the form of the angular wave functions, show that the total electron density, 2(2px)+2(2py)+2(2pz) , is spherically symmetric (that is, it is independent of the angles and ). The neon atom, which has two electrons in each 2p orbital, is also spherically symmetric. (b) The same result as in part (a) applies to d orbitals, thus a filled or half-filled subshell of d orbitals is spherically symmetric. Identify the spherically symmetric atoms or ions among the following: F , Na, Si, S2,Ar+ , Ni, Cu, Mo, Rh, Sb, W, Au.
Using Table 5.2, write down the mathematical expression for the 2px wave function for an electronically excited H atom. Estimate the probability of finding the 2px electron if you look in a cubical box of volume of 0.8(pm)3 centered at a distance of 0.5001010m in the =/2 , =0 direction. Does this probability change as you change ? At what angles is the probability of finding the electron smallest and at what angles is the probability the largest? (Note that =2 is the same location as =0 , so don’t double count.)
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?
What are the values of E, L, and Lz for an F8+ atom whose electron has the following wavefunctions, listed as n,l,ml? a 1,0,0 b 3,2,2c 2,1,1d 9,6,3.
The photoelectric effect is used today to make light-sensitive detectors; when light hits a sample of metal in a sealed compartment, a current of electrons may flow if the light has the proper wavelength. Cesium is a desirable component for such detectors. Why?

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note that a probability map is not the same as a balloon model is a probability map of a single s orbital in cross-section is a probability map of a single p orbital in cross-section (a) (b) (c) (d)