Physical Chemistry , 1st ed.

where and are varied (but ris still constant!), the Hamiltonian opera- tor is Hˆ  2 I 2     2  2 cot     s ...

differential terms in the Hamiltonian contain , so no simplification is gained. (The third term is not a differential in terms ...

Now the two parts of the solution for equation 11.46 can be combined to get the entire solution for 3-D rotational motion. The a ...

Each integral can be solved separately. The first integral, over , is easily shown to be  2   0 d 02  2  0  2  Th ...

Example 11.17 The carbon molecule buckminsterfullerene, C 60 , can be approximated as a sphere, and the electrons of the molecul ...

The difference in the energies is E4.96 10 ^19 J Using Eh , it can be shown that this energy difference corresponds to the ...

Solution According to equation 11.53, the total angular momentum is dependent only on and .For 4 and 5, the angular momenta ...

Since the values ofLxand Lyare indeterminate for specified and m, the graphical representations of Figure 11.14 are better rep ...

Solution The complete spherical harmonic 3, 3 is given by 3, 3  e^3 isin^3  Let us consider the total angular momentum f ...

^2 (12 sin^3 )  8 7 2 0  e^3 i  12 ^2 3, 3 So, invoking the postulate that the value of an observable is equal to ...

for their quantized values depends on the system.Average values,rather than quantized values, may be all that can be determined. ...

In the case of the hydrogen atom, the potential energy is not zero. There is an interaction between the electron and the nucleus ...

The influence of the spherical harmonics part of the complete wavefunction is seen in the second term on the left. Although this ...

For convenience, several of the first few wavefunctions are listed in Table 11.4 along with their respective n,, and mquantum ...

quantum number.Because n^2 wavefunctions have the same quantum number n, the degeneracy of each energy state of the hydrogen ato ...

which is easily shown to be, in units of wavenumbers and to four significant figures,  8 e  4 (^20)  h^2 109,700 cm^1 This ...

of the hydrogen atom. The transitions appear at different wavelengths of light, however. Example 11.22 Predict the wavelength of ...

Orbitals are designated by pairing the value of the principal quantum number and the letter representing the value of:1s,2s,2p, ...

Wavefunctions for hydrogen-like systems, determined by quantum num- bers, can be labeled with those quantum numbers. Therefore, ...

where ais the same constant previously defined for the Rfunctions. Since it is defined as a group of constants,aitself is a cons ...