Chapter 8: Q49E (page 342)
Determine the electronic configuration for phosphorus, germanium and cesium.
Short Answer
Phosphorus (15) , Germanium (32),
Cesium (55) .
Chapter 8: Q49E (page 342)
Determine the electronic configuration for phosphorus, germanium and cesium.
Phosphorus (15) , Germanium (32),
Cesium (55) .
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Get started for freeThe Slater determinant is introduced in Exercise 42. Show that if states and of the infinite well are occupied. with the particle in state being spin up and the one in being spin down. then the Slater determinant yields the antisymmetric multiparticle state: .
A lithium atom has three electrons. These occupy individual particle states corresponding to the sets of four quantum numbers given by .
Using to represent the individual-particle states when occupied by particle . Apply the Slater determinant discussed in Exercise 42 to find an expression for an antisymmetric multiparticle state. Your answer should be sums of terms like .
Question: What if electrons were spin instead of spin . What would be Z for the first noble gas?
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.
Question: Bearing in mind its limiting cases of 1 and 2 mentioned in section 8.8, how would you describe the significance of the Lande g-factor
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