Solution of the Schrödinger wave equation for the hydrogen atom results in a set of functions (orbitals) that describe the behavior of the electron. Each function is characterized by three quantum numbers: n, I, and my. If the value of n = 2 The quantum number / can have values from to The total number of orbitals possible at the n = 2 energy level is If the value of 1 = 2 The quantum number m, can have values from to The total number of orbitals possible at the / = 2 sublevel is Submit Answer Retry Entire Group 9 more group attempts remaining

Solution of the Schrödinger wave equation for the hydrogen atom results in a set of functions (orbitals) that describe the behavior of the electron. Each function is characterized by three quantum numbers: n, I, and my. If the value of n = 2 The quantum number / can have values from to The total number of orbitals possible at the n = 2 energy level is If the value of 1 = 2 The quantum number m, can have values from to The total number of orbitals possible at the / = 2 sublevel is Submit Answer Retry Entire Group 9 more group attempts remaining

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

Chapter4: Introduction To Quantum Mechanics

Section: Chapter Questions

Problem 39P: Chapter 3 introduced the concept of a double bond between carbon atoms, represented by C=C , with a...

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(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.
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.)
Suppose that the spin quantum number did not exist, and therefore only one electron could occupy each orbital of a many-electron atom. Give the atomic numbers of the first three noble-gas atoms in this case.
The helium ion He+ is a one-electron system whose wave functions and energy levels are obtained from those for H by changing the atomic number to Z=2 . Calculate the average distance of the electron from the nucleus in the 2s orbital and in the 2p orbital. Compare your results with those in Problem 11 and explain the difference.
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?
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?
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.
What are quantum numbers? What information do we get from the quantum numbers n, l, and ml? We define a spin quantum number (ms), but do we know that an electron literally spins?
State which of the following orbitals cannot exist according to the quantum theory: 3p, 4s, 2f, and 1p. Briefly explain your answers.
When metallic sodium is dissolved in liquid sodium chloride, electrons are released into the liquid. These dissolved electrons absorb light with a wavelength near 800 nm. Suppose we treat the positive ions surrounding an electron crudely as defining a three-dimensional cubic box of edge L, and we assume that the absorbed light excites the electron from its ground state to the first excited state. Calculate the edge length L in this simple model.
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.