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Chapter 8: Q17CQ (page 338)
Question: What if electrons were spin instead of spin . What would be Z for the first noble gas?
Answer
The value of z = 4.
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What angles might the intrinsic angular momentum vector make with the z-axis for a deuteron? (See Table 8.1)
Is intrinsic angular momentum "real" angular momentum? The famous Einstein-de Haas effect demonstrates it. Although it actually requires rather involved techniques and high precision, consider a simplified case. Suppose you have a cylinder in diameter hanging motionless from a thread connected at the very center of its circular top. A representative atom in the cylinder has atomic mass 60 and one electron free to respond to an external field. Initially, spin orientations are as likely to be up as down, but a strong magnetic field in the upward direction is suddenly applied, causing the magnetic moments of all free electrons to align with the field.
(a) Viewed from above, which way would the cylinder rotate?
(b) What would be the initial rotation rate?
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.
Question: A good electron thief needs a trap at low energy to entice its prey. A poor electron shepherd will have at least some of its flock dangling out at high energy, consider row 2 and 5 in the periodic table. Why should fluorine, in row 2, is less reactive than rubidium, in row 5?
The general form for symmetric and antisymmetric wave functions is but it is not normalized.
(a) In applying quantum mechanics, we usually deal with quantum states that are "orthonormal." That is, if we integrate over all space the square of any individual-particle function, such as, we get 1, but for the product of different individual-particle functions, such as, we get 0. This happens to be true for all the systems in which we have obtained or tabulated sets of wave functions (e.g., the particle in a box, the harmonic oscillator, and the hydrogen atom). Assuming that this holds, what multiplicative constant would normalize the symmetric and antisymmetric functions?
(b) What valuegives the vectorunit length?
(c) Discuss the relationship between your answers in (a) and (b)?
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