14. The picture below shows a cross-section of the electron density of an orbital (dark areas represent electron density). a) Which orbital is represented? Identify the features that allow you to identify the orbital unambiguously. (2) b) In the coordinate system to the right, qualitatively draw the corresponding radial wave function. (3) intensity of wave function distance r from nucleus

14. The picture below shows a cross-section of the electron density of an orbital (dark areas represent electron density). a) Which orbital is represented? Identify the features that allow you to identify the orbital unambiguously. (2) b) In the coordinate system to the right, qualitatively draw the corresponding radial wave function. (3) intensity of wave function distance r from nucleus

Principles of Modern Chemistry

8th Edition

ISBN:9781305079113

Author:David W. Oxtoby, H. Pat Gillis, Laurie J. Butler

Publisher:David W. Oxtoby, H. Pat Gillis, Laurie J. Butler

Chapter5: Quantum Mechanics And Atomic Structure

Section: Chapter Questions

Problem 44AP: The energy needed to ionize an atom of element X when it is in its most stable state is 500kJmol1 ....

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Estimate the probability of finding an electron which is excited into the 2s orbital of the H atom, looking in a cubical box of volume 0.751036m3 centered at the nucleus. Then estimate the probability of finding the electron if you move the volume searched to a distance of 105.8 pm from the nucleus in the positive z direction. (Note that since these volumes are small, it does not matter whether the volume searched is cubical or spherical.)
Sketch the major features (number of peaks and relative intensities for the peaks) of the expected photoelectron spectrum for atoms of nitrogen.
• identify an orbital (as 1s, 3p, etc.) from its quantum numbers, or vice versa.
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?
Using Fig. 2-30, list the elements (ignore the lanthanides and actinides) that have ground-state electron configurations that differ from those we would expect from their positions in the periodic table.
Give a brief wave description of light. What are two characteristics of light waves?
The wave function of an electron in the lowest (that is, ground) state of the hydrogen atom is (r)=( 1 a 0 3 )1/2exp(r a 0 )ao=0.5291010m (a) What is the probability of finding the electron inside a sphere of volume 1.0pm2 , centered at the nucleus (1pm=1012m) ? (b) What is the probability of finding the electron in a volume of 1.0pm2 at a distance of 52.9 pm from the nucleus, in a fixed but arbitrary direction? (c) What is the probability of finding the electron in a spherical shell of 1.0 pm in thickness, at a distance of 52.9 pm from the nucleus?
The energy needed to ionize an atom of element X when it is in its most stable state is 500kJmol1 . However, if an atom of X is in its lowest excited state, only 120kJmol1 is needed to ionize it. What is the wavelength of the radiation emitted when an atom of X undergoes a transition from the lowest excited state to the ground state?
Chapter 3 introduced the concept of a double bond between carbon atoms, represented by C=C , with a length near 1.34 Å. The motion of an electron in such a bond can be treated crudely as motion in a one-dimensional box. Calculate the energy of an electron in each of its three lowest allowed states if it is confined to move in a one-dimensional box of length 1.34 Å. Calculate the wavelength of light necessary to excite the electron from its ground state to the first excited state.
Construct an energy level diagram showing all orbitals for the hydrogen atom up to n=5, labeling each orbital with its appropriate quantum numbers. How many different orbitals are in each shell?
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.)
The cesium atom has the lowest ionization energy, 375.7kJmol1 , of all the neutral atoms in the periodic table. What is the longest wavelength of light that could ionize a cesium atom? In which region of the electromagnetic spectrum does this light fall?