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Chapter 8: Q5CQ (page 338)
The neutron comprises multiple charged quarks. Can a particle that is electrically neutral but really composed of charged constituents have a magnetic dipole moment? Explain your answer.
Yes, an electrically neutral particle composed of charged constituents has a magnetic dipole moment.
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To determine the value of Z at which the relativistic effects might affect energies and whether it applies to all orbiting electrons or to some more than others, also guess if it is acceptable to combine quantum mechanical results.
Whether adding spins to get total spin, spin and orbit to get total angular momentum, or total angular momenta to get a "grand total" angular momentum, addition rules are always the same: Given and . Where is an angular momentum (orbital. spin. or total) and a quantum number. the total is , where may take on any value between and in integral steps: and for each value of . where may take on any ofI possible values in integral steps from for Since separately there would be possible values for and I for . the total number of stales should be . Prove it: that is, show that the sum of the values for over all the allowed values for is . (Note: Here we prove in general what we verified in Example for the specialcase .)
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?
The general rule for adding angular momenta is given in Exercise 66, when adding angular momenta with and
(a) What are the possible values of the quantum number and the total angular momentum .
(b) How many different states are possible and,
(c) What are the values for each of these states?
Question: Discuss what is right or wrong about the following statement:
Nobel gases correspond to full shells.
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