True or false a. Bohr model can be applied to atoms with 2 electrons. T F b. An eigenvalue is a function c. The photoelectric effect supports the idea that light is a bunch of particles T F T F d. The Hamiltonian operator H is equal to del?T F e. The radius of the first orbit in Hydrogen is ao T F f. The energy of a free particle is continuous T F g. An example of an eigenfunction of the momentum operator is x" . Show work. T F

True or false a. Bohr model can be applied to atoms with 2 electrons. T F b. An eigenvalue is a function c. The photoelectric effect supports the idea that light is a bunch of particles T F T F d. The Hamiltonian operator H is equal to del?T F e. The radius of the first orbit in Hydrogen is ao T F f. The energy of a free particle is continuous T F g. An example of an eigenfunction of the momentum operator is x" . Show work. T F

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 9P: Use the mathematical expression for the 2pz wave function of a one-electron atom (see Table 5.2) to...

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Defend and criticize Bohrs model. Why was it reasonable that such a model was proposed, and what evidence was there that it "works"? Why do we no longer "believe" in it?
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6.32 What are the mathematical origins of quantum numbers?
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?
How does probability fit into the description of the atom?
Imagine a world in which the rule for the l quantum number is that values start with 1 and go up to n. The rules for the n and mi quantum numbers are unchanged from those of our world. Write the quantum numbers for the first two shells (i.e., n = 1 and n = 2).
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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.)
How are the Bohr model and the quantum mechanical model of the hydrogen atom similar? How are they different?
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?
Suppose that the spin quantum number could have the values 12,0 and 12 . Assuming that the rules governing the values of the other quantum numbers and the order of filling sublevels were unchanged, (a) what would be the electron capacity of an s sublevel? a p sublevel? a d sublevel? (b) how many electrons could fit in the n=3 level? (c) what would be the electron configuration of the element with atomic number 8? 17?
Consider the orbitals shown here in outline. (a) What is the maximum number of electrons contained in an orbital of type (x)? Of type (y)? Of type (z)? (b) How many orbitals of type (x) are found in a shell with n=2? How many of type (y)? How many of type (z)? (c) Write a set of quantum numbers for an electron in an orbital of type (x) in a shell with n=4, of an orbital of type (y) in a shell with n=2. Of an orbital of type (z) in a shell with n=3. (d) What is the smallest possible n value for an orbital of type (x)? Of type (y)? Of type (z)? (e) What are the possible I and ml values for an orbital of type (x)? Of type (y)? Of type (z)?