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Chapter 8: Q23CQ (page 339)
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
Answer
X-rays do not start at hydrogen or helium because all of the electrons are electrons.
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What is the angle between the spins in a triplet state?
A beam of identical atoms in their ground state is sent through a Stem-Gerlach apparatus and splits into three lines. Identify possible sets of their total spin and total orbital angular momentum? Ignore possibilities in which sT is 2 or higher.
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.
The electron is known to have a radius no larger than . If actually produced by circulating mass, its intrinsic angular momentum of roughlywould imply very high speed, even if all that mass were as far from the axis as possible.
(a) Using simply(from |r × p|) for the angular momentum of a mass at radius r, obtain a rough value of p and show that it would imply a highly relativistic speed.
(b) At such speeds,andcombine to give(just as for the speedy photon). How does this energy compare with the known internal energy of the electron?
Question: Huge tables of characteristic X-rays start at lithium. Why not hydrogen or helium?
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