Here is a sketch of the radial probability distribution of three orbitals: 0.0020 probability 0.0015 0.0010- 0.0005 500 1000 1500 2000 2500 3000 distance from nucleus (pm) Use this sketch to answer the following questions. What is the most likely distance from the nucleus for an electron in orbital A? Note: your answer must be within 50 pm of the exact answer to be graded correct. List the orbitals in order of increasing energy: Suppose all three orbitals were inner orbitals of an atom. In which orbital would an electron be most effective at screening the charge of the nucleus from the outer electrons? ☐ pm (choose one) -B 0,0.... G

Here is a sketch of the radial probability distribution of three orbitals: 0.0020 probability 0.0015 0.0010- 0.0005 500 1000 1500 2000 2500 3000 distance from nucleus (pm) Use this sketch to answer the following questions. What is the most likely distance from the nucleus for an electron in orbital A? Note: your answer must be within 50 pm of the exact answer to be graded correct. List the orbitals in order of increasing energy: Suppose all three orbitals were inner orbitals of an atom. In which orbital would an electron be most effective at screening the charge of the nucleus from the outer electrons? ☐ pm (choose one) -B 0,0.... G

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 55AP: The energies of macroscopic objects, as well as those of microscopic objects, are quantized, but the...

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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?
• 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?
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?
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?
6.32 What are the mathematical origins of quantum numbers?
ow does probability ?t into the description of the atom?
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?
6.106 When Bohr devised his model for the atom, was he using deductive or inductive reasoning? Explain your answer.
How does probability fit into the description of the atom?
(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.
What are the allowed values for each of the four quantum numbers: n, l, ml, and ms?