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Chapter 8: Q18CQ (page 338)
Question: As indicated to remove one of the helium’s electrons requires of energy when orbiting ? Why or why not?
Answer
No, the Energy of orbiting electron is not .-24.6 ev
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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?
Does circulating charge require both angular momentum and magnetic? Consider positive and negative charges simultaneously circulating and counter circulating.
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
Using a beam of electrons accelerated in an X-ray tube, we wish to knock an electron out of the shell of given element in a target. Section \(7.8\) gives the energies in a hydrogen like atom as . Assume that for fairly high Z , aK-shell electron can be treated as orbiting the nucleus alone.
(a) A typical accelerating potential in an X-ray tube is . In roughly how high aZcould a hole in the K -shell be produced?
(b) Could a hole be produced in elements of higher Z?
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