Physical Chemistry , 1st ed.

b.For the Be^3 nucleus, the solution to the problem is along similar lines but now the nuclear charge for the beryllium atom mu ...

363 0 Distance from nucleus (Å) 8 4  (^2) r R (2 s) (^2)  4  (^2) r R (2 p) (^2)  0 Distance from nucleus (Å) 15 4  (^2) ...

364 + + + + + + px py + + + + + + – pz + – – dxz dyz dxy dx 2  y 2 dz^2 Figure 11.21 The 90% boundary plo ...

Example 11.25 a.What is the average value of the total angular momentum for  3 pfor the hydrogen atom? b.Is there an easier way ...

systems, like molecules (for smaller molecules in practice, and for larger mol- ecules at least in theory). Because this is far ...

11.2 Classical Harmonic Oscillator 11.1.Convert 3.558 mdyn/Å into units of N/m. 11.2.A swinging pendulum has a frequency of 0.27 ...

force constant. D deuterium (^2 H). Assume that the force constant remains the same. 11.6 2-D Rotations 11.22.Why can’t the qua ...

11.44.Calculate the difference between the Bohr radius de- fined as aand the Bohr radius defined as a 0. 11.45.To four significa ...

12 W E HAVE SEEN HOW QUANTUM MECHANICS provides tools for understanding some simple systems, up to and including the hydro- gen ...

12.2 Spin Not long before quantum mechanics was developed, an important experimen- tal observation was made. In 1922, Otto Stern ...

spin angular momentum, with s, an orbital that has 0.) The eigenvalue equations are therefore Sˆ^2 s(s1)^2  (12.1) Szms ...

differentiate between orbitalangular momentum and spinangular momen- tum. Both observables are angular momenta, but they arise f ...

Spin is unaffected by any other property or observable of the electron, and the spin component of a one-electron wavefunction is ...

where the other variables have been defined in the previous chapter. The 2 in the numerator of each of the first two terms is du ...

same level that one can know such observables for the hydrogen atom—if one has the tools. Example 12.3 Assume that the helium wa ...

which is low by 37.8% compared to experiment. Ignoring the repulsion between the electrons leads to a significant error in the t ...

Approximate wavefunction Total z-component spin He(1s 1 )(1s 2 )  1 He(1s 1 )(1s 2 ) 0 He(1s 1 )(1s 2 ) 0 He(1s 1 ...

The switch in order of writing the labels 1 and 2 implies that the two electrons are exchanged. Electron 1 now has the coordinat ...

The term 1/ 2 multiplies the entire determinant, like it multiplies the entire wavefunction in equation 12.8. Such determinant ...

and in all cases the determinant is exactly zero, implying that the overall wave- function does not exist. On this basis, one co ...