Learning Materials
Features
Discover
Chapter 8: Q2CQ (page 338)
Does circulating charge require both angular momentum and magnetic? Consider positive and negative charges simultaneously circulating and counter circulating.
No, the circulating charge does not require both angular momentum and magnetic.
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
Figureshows the Stern-Gerlach apparatus. It reveals that spin-particles have just two possible spin states. Assume that when these two beams are separated inside the channel (though still near its centreline). we can choose to block one or the other for study. Now a second such apparatus is added after the first. Their channels are aligned. But the second one is rotated about the-axis by an angle \(\phi\) from the first. Suppose we block the spin-down beam in the first apparatus, allowing only the spin-up beam into the second. There is no wave function for spin. but we can still talk of a probability amplitude, which we square to give a probability. After the first apparatus' spin-up beam passes through the second apparatus, the probability amplitude iswhere the arrows indicate the two possible findings for spin in the second apparatus.
(a) What is the probability of finding the particle spin up in the second apparatus? Of finding it spin down? Argue that these probabilities make sense individually for representative values ofand their sum is also sensible.
(b) By contrasting this spin probability amplitude with a spatial probability amplitude. Such as. Argue that although the arbitrariness ofgives the spin cases an infinite number of solves. it is still justified to refer to it as a "two-state system," while the spatial case is an infinite-state system.
Slater Determinant: A convenient and compact way of expressing multi-particle states of anti-symmetric character for many fermions is the Slater determinant:
It is based on the fact that for N fermions there must be Ndifferent individual-particle states, or sets of quantum numbers. The ith state has spatial quantum numbers (which might be , and ) represented simply by and spin quantum number . Were it occupied by the ith particle, the slate would be a column corresponds to a given state and a row to a given particle. For instance, the first column corresponds to individual particle state . Where jprogresses (through the rows) from particle 1 to particle N. The first row corresponds to particle I. which successively occupies all individual-particle states (progressing through the columns). (a) What property of determinants ensures that the multiparticle state is 0 if any two individual particle states are identical? (b) What property of determinants ensures that switching the labels on any two particles switches the sign of the multiparticle state?
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).
Question: As indicated to remove one of the helium’s electrons requires of energy when orbiting ? Why or why not?
Question: In the Stern-Gerlach experiment how much would a hydrogen atom emanating from a 500 K ovenbe deflected in traveling 1 m through a magnetic field whose rate of change is 10 T/m?
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