Which of the following set of quantum numbers (ordered n, f, me, m.) are possible for an electron in an atom? Check all that apply. ▸ View Available Hint(s) 3,2, -3, 1/2 3, 2, 1,-1 2,4, 1,-1/2 4, 2, 1,-1/2 5, 2, 1,-1/2 -4, 3, 1, 1/2 5, 3, 4, 1/2 3, 2, 2, -1/2

Which of the following set of quantum numbers (ordered n, f, me, m.) are possible for an electron in an atom? Check all that apply. ▸ View Available Hint(s) 3,2, -3, 1/2 3, 2, 1,-1 2,4, 1,-1/2 4, 2, 1,-1/2 5, 2, 1,-1/2 -4, 3, 1, 1/2 5, 3, 4, 1/2 3, 2, 2, -1/2

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 5P: Estimate the probability of finding an electron which is excited into the 2s orbital of the H atom,...

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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.)
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?
A particle of mass m is placed in a three-dimensional rectangular box with edge lengths 2L, L, and L. Inside the box the potential energy is zero, and outside it is infinite; therefore, the wave function goes smoothly to zero at the sides of the box. Calculate the energies and give the quantum numbers of the ground state and the first five excited states (or sets of states of equal energy) for the particle in the box.
Answer the following questions. (a) What characteristic of an atomic orbital does the quantum number ms describe? (b) Does a photon with a frequency of 35.8 Hz have more or less energy than one with a frequency of 125 Hz? (c) How many orbitals can be associated with the following set of quantum numbers:n=3, l=2? (d) Is a sample of ZnCl2 containing the Zn2+ ion diamagnetic?
(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.
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?
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.
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.
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.)
• identify an orbital (as 1s, 3p, etc.) from its quantum numbers, or vice versa.
The energies of macroscopic objects, as well as those of microscopic objects, are quantized, but the effects of the quantization are not seen because the difference in energy between adjacent states is so small. Apply Bohr’s quantization of angular momentum to the revolution of Earth (mass6.01024kg) , which moves with a speed of 3.0104ms1 in a circular orbit (radius1.51011m) about the sun. The sun can be treated as fixed. Calculate the value of the quantum number n for the present state of the Earthsun system. What would be the effect of an increase in n by 1?
Suppose that the spin quantum number had three allowed values (ms=0,+12,12) . Give the atomic numbers of the first three noble-gas atoms in this case.