Chapter 8: Problem 49
Write the electronis configurations for phosphorus. germanium. and cesium.
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Key Concepts
These are the key concepts you need to understand to accurately answer the question.
Chapter 8: Problem 49
Write the electronis configurations for phosphorus. germanium. and cesium.
These are the key concepts you need to understand to accurately answer the question.
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Get started for freeCompare and contrast the angular momentum and magnetic moment related to or bital mot ion with those that ane intrinsic.
Whether a neutral whole atom behaves as a boson or a fermion is independent of \(Z\), instead depending entirely on the number of neutrons in its nucleus. Why? Whatrs it about this number that determines whether the atom is a boson or a fernion?
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 tlock dangling out at high energy. Consider rows 2 and 5 in the periodic table. Why should fluorine, in row \(2,\) be more reactive than iodine. in row 5 , while lithium, in row 2 , is less reactive than \mathrm{\\{} u b i d i u m , ~ i n ~ r o w ~ 5 ?
As is done for helium in Table 8.3 , determine for a carton atom the various states allowed according to \(\angle S\) coupling. The coupling is between carbon's two \(2 p\) electrons (its filled 2 s subshell not participating). one of which always remains in the \(2 p\) state. Consider cases in which the other is as high as the \(3 d\) level. (Note: When both electrons are in the \(2 p\), the exclusion principle Iestricts the number of states. The only allowed states are those in which \(s_{r}\) and \(\ell_{T}\) are both even or both odd.)
Exercise 44 gives an antisymmetric multiparticle state for two particles in a box with opposite spins. Another antisymmetric state with spins opposite and the same quantum numbers is $$ \psi_{n}\left(x_{1}\right) \downarrow \psi_{n}\left(x_{2}\right) \uparrow-\psi_{n}\left(x_{1}\right) \uparrow \psi_{n}\left(x_{2}\right) \downarrow $$ Refer to these states as \(\mid\) and 11 . We have tended to characterize exchange symmetry as to whether the state's sign changes when we swap particle labels. but we could achieve the same result by instead swapping the particles' stares, specifically the \(n\) and \(n^{\prime}\) in equation \((8-22)\). In this exercise. we look at swapping only parts of the state-spatial or spin. (a) What is the exchange symmeiry - symmetric (unchanged). antisymmetric (switching sign), or neither-of multiparticle states 1 and \(\mathrm{II}\) with respect to swapping spatial states alone? (b) Answer the same question. but with respect to swapping spin states/arrows alone. (c) Show that the algebraic sum of states 1 and \(\mathrm{II}\) may be written \(\left(\psi_{n}\left(x_{1}\right) \psi_{n}\left(x_{2}\right)-\psi_{n}\left(x_{1}\right) \psi_{n}\left(x_{2}\right)\right)(\downarrow T+\uparrow \downarrow)\) where the left arrow in any couple represents the spin of particle 1 and the right arrow that of particle 2 (d) Answer the same questions as in parts \((a)\) and (b). but for this algebraic sum. (e) Is the sum of states I and 11 still antis ymmetric if we swap the particles? total-spatial plus spin -states? (f) If the two particles repel each other, would any of the three multiparticle states - l. II, and the sum - be preferred? Explain.
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