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Nuclear spin statistical weights

When nuclear spin is included the total wave function p for a molecule is modified from that of Equation (1.58) to [Pg.128]

For a symmetrical diatomic or linear polyatomic molecule with two, or any even [Pg.129]

Equation (1.48) shows that, for I =, space quantization of nuclear spin angular momentum results in the quantum number Mj taking the values 5 or — 5. The nuclear spin wave function J/ is usually written as a or /i, corresponding to Mj equal to 5 or —5, [Pg.129]

Although the a(l)a(2) and /i(l)/i(2) wave functions are clearly symmetric to interchange of the 1 and 2 labels, the other two functions are neither symmetric nor antisymmetric. For this reason it is necessary to use instead the linear combinations 2 / [a(l)/i(2) + /i(l)a(2)] and 2 / [a(l)/i(2) — /i(l)a(2)], where 2 is a normalization constant. Then three of the four nuclear spin wave functions are seen to be symmetric (5 ) to nuclear exchange and one is antisymmetric (a)  [Pg.130]

In general, for a homonuclear diatomic molecule there are (21+ )(/+1) symmetric and (21+ 1)/antisymmetric nuclear spin wave functions therefore [Pg.130]

For a symmetrical (D ) diatomic or linear polyatomic molecule with two, or any even number, of identical nuclei having the nuclear spin quantum number (see Equation 1.47) I = n + where n is zero or an integer, exchange of any two which are equidistant from the centre of the molecule results in a change of sign of i/c which is then said to be antisymmetric to nuclear exchange. In addition the nuclei are said to be Fermi particles (or fermions) and obey Fermi Dirac statistics. However, if / = , p is symmetric to nuclear exchange and the nuclei are said to be Bose particles (or bosons) and obey Bose-Einstein statistics. [Pg.129]

We will now consider the consequences of these rules in the simple case of H2. In this molecule both i// , whatever the value of v, and ij/e, in the ground electronic state, are symmetric to nuclear exchange so we need consider only the behaviour of Since [Pg.129]


These limitations lead to electron spin multiplicity restrictions and to differing nuclear spin statistical weights for the rotational levels. Writing the electronic wavefunction as the product of an orbital fiinction and a spin fiinction there are restrictions on how these functions can be combined. The restrictions are imposed by the fact that the complete function has to be of synnnetry... [Pg.174]

Figure 5.18 Nuclear spin statistical weights (ns stat wts) of rotational states of various diatomic molecules a, antisymmetric s, symmetric o, ortho p, para and rotational, nuclear spin... Figure 5.18 Nuclear spin statistical weights (ns stat wts) of rotational states of various diatomic molecules a, antisymmetric s, symmetric o, ortho p, para and rotational, nuclear spin...
All other homonuclear diatomic molecules with / = for each nucleus, such as F2, also have ortho and para forms with odd and even J and nuclear spin statistical weights of 3 and 1, respectively, as shown in Figure 5.18. [Pg.130]

The nuclear spin statistical weight factors for " NH3 are determined in Section 8.4.1 of Ref. [3] and we do not repeat the derivation here. The results are summarized in Table 2. The 24 nuclear spin functions (see Chapter 8 in Ref. [3])... [Pg.219]

Nuclear spin statistical weights were discussed in Section 5.3.4 and the effects on the populations of the rotational levels in the v = 0 states of H2, 19F2, 2H2, 14N2 and 1602 illustrated as examples in Figure 5.18. The effect of these statistical weights in the vibration-rotation Raman spectra is to cause a J" even odd intensity alternation of 1 3 for H2 and 19F2 and 6 3 for 2H2 and 14N2 for 1602, all transitions with J" even are absent. It is for the... [Pg.153]

For the thermal unimolecular reaction the expression (71) is extended by a further explicit summation over the symmetry index F with W(E, J, F) with a nuclear spin statistical weight gK( )- The integral in equation (71) can be calculated, in the regular limit, using the approximation in equation (98) ... [Pg.2720]

We now consider these terms separately. As far as nuclear energy is concerned, it may be taken equal to zero. The nuclear partition function then becomes fn = Qna, where Qub is the nuclear spin statistical weight. Since the allowed rotational levels are dependent upon the nuclear spin wave functions, as we have seen in section 14c, it is convenient to combine the nuclear spin statistical weight with the rotational partition function, and write... [Pg.292]


See other pages where Nuclear spin statistical weights is mentioned: [Pg.174]    [Pg.176]    [Pg.180]    [Pg.128]    [Pg.153]    [Pg.187]    [Pg.212]    [Pg.219]    [Pg.235]    [Pg.128]    [Pg.85]    [Pg.109]    [Pg.125]    [Pg.335]    [Pg.174]    [Pg.176]    [Pg.180]    [Pg.100]    [Pg.18]    [Pg.360]    [Pg.2717]    [Pg.2717]    [Pg.267]    [Pg.184]   
See also in sourсe #XX -- [ Pg.128 ]

See also in sourсe #XX -- [ Pg.128 ]




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