Learning Materials
Features
Discover
Chapter 8: 79E (page 344)
In its ground state, nitrogen's 2p electrons interact to produce . Given Hund's rule, how might the orbit at angular momenta of these three electrons combine?
The total orbital quantum number lT are.
Over 30 million students worldwide already upgrade their learning with Vaia!
All the tools & learning materials you need for study success - in one app.
Get started for free
A Simple Model: The multielectron atom is unsolvable, but simple models go a long way. Sectiongives energies and orbit radii forone-electron/hydrogenlike atoms. Let us see how useful these are by considering lithium.
(a) Treat one of lithium'selectrons as a single electron in a one-electron atom ofrole="math" localid="1659948261120" . Find the energy and orbit radius.
(b) The otherelectron being in the same spatial state. must have the same energy and radius, but we must account for the repulsion between these electrons. Assuming they are roughly one orbit diameter apart, what repulsive energy would they share, and if each claims half this energy. what would be the energies of these two electrons?
(c) Approximately what charge does lithium's lone valence electron orbit, and what radius and energy would it have?
(d) Is in reasonable to dismiss the role of theelectrons in chemical reactions?
(e) The actual energies of lithium's electrons are about(twice, of course) and. How good is the model?
(f) Why should the model's prediction for the valence electron's energy differ in the direction it does from the actual value?
The total-spin singlet state for two electrons has one spin up and one down, but one of the triplet states does. too. What is the difference?
Question: As the 2p levels fill from Z = 5 to 10 the element's first ionization energies tend to increase. But as the figure below clearly indicates it is slightly easier to remove an electron from Z = 8 oxygen than from Z = 7 nitrogen. What might explain this?
The wave functions for the ground and first excited states of a simple harmonic oscillator are and. Suppose you have two particles occupying these two states.
(a) If distinguishable, an acceptable wave function would berole="math" localid="1659955524302" . Calculate the probability that both particles would be on the positive side of the origin and divide by the total probability for both being found over all values of,. (This kind of normalizing-as-we-go will streamline things.)
(b) Suppose now that the particles are indistinguishable. Using thesymbol to reduce your work. calculate the same probability ratio, but assuming that their multiparticle wave function is either symmetric or antisymmetric. Comment on your results.
As is done for helium in Table 8.3, determine for a carbon atom the various states allowed according to LS coupling. The coupling is between carbon's two 2p electrons (its filled 2s subshell not participating), one or which always remains in the 2p state. Consider cases in which the other is as high as the 3d level. (Note: Well both electrons are in the 2p, the exclusion principle restricts the number of states. The only allowed states are those in whichand are both even or both odd).
What do you think about this solution?
We value your feedback to improve our textbook solutions.
Explanations 
Textbooks 
Exams 
GCSE 
IGCSE 
AS 
A Level 
International A Level 
University Admissions Tests 
Flashcards 
Vaia AI 
Notes 
Study Plans 
Study Sets 
Find a job 
Find a degree 
Student Deals 
Magazine 
Mobile App