Reduced mass atomic

Molecule Reduced mass (atomic units) Dissociation energy kcals Zero-point energy kcals Inter- nuclear distance A Moment of inertia gmcm2 X io40 Force constant dynes cm l X io 8 Vibrational frequency cm l... 

Since the reduced mass depends only on the masses of the atoms (1/p = + Mm for a diatomic), which... 

For each pair of interacting atoms (/r is their reduced mass), three parameters are needed D, (depth of the potential energy minimum, k (force constant of the par-tictilar bond), and l(, (reference bond length). The Morse ftinction will correctly allow the bond to dissociate, but has the disadvantage that it is computationally very expensive. Moreover, force fields arc normally not parameterized to handle bond dissociation. To circumvent these disadvantages, the Morse function is replaced by a simple harmonic potential, which describes bond stretching by Hooke s law (Eq. (20)). 

E10.6 For the diatomic molecule Na2, 5 = 230.476 J-K-1-mol" at T= 300 K, and 256.876 J-K-,-mol-1 at T= 600 K. Assume the rigid rotator and harmonic oscillator approximations and calculate u, the fundamental vibrational frequency and r, the interatomic separation between the atoms in the molecule. For a diatomic molecule, the moment of inertia is given by l pr2, where p is the reduced mass given by... 

The quantity p (mu) is called the effective mass of the molecular vibration (some people call it the reduced mass ). As we anticipated, the frequency is higher for stiff bonds (large k) and low atomic masses (low p). We see that, by measuring... 

The reduced mass p of two atoms connected by a covalent bond is p = + m-d-... 

Ans. (a) The mass number changes by 28 units in this series, corresponding to seven alpha particles (7x4 = 28). (b) The seven alpha particles emitted would have reduced the atomic number by 14 units if no beta particles had been emitted since the atomic number is reduced by only 10 units, four (14 - 10) beta particles are also emitted, (c) It is impossible to tell from these data alone what the order of emission is. (d) It is impossible to tell the number of gamma particles emitted, since emission of a gamma particle does not change either the mass number or the atomic number. 

In the foregoing, U is the interaction potential, M is the reduced mass of the colliding system, ftk and ftk are respectively the momentum of the projectile before and after the collision, ig and in are respectively the wavefunctions of the atom (or molecule) in the ground and nth excited states, and the volume element dt includes the atomic electron and the projectile. Since U for charged-particle impact may be represented by a sum of coulombic terms in most cases, Eq. (4.11) can be written as (Bethe, 1930 Inokuti, 1971)... 

Atomic isotopes help detection so that the shift for 13 CO is perfectly predictable and isotope ratios are known from various sources, as we shall see later on. The change in the rotational constant with reduced mass is easily calculated and hence the change in the frequency of the J = J = 0 can be calculated, as we saw in Section 3.3. 

The quantity 2b2 is the force constant of the corresponding bond with h 7rH2/j,)1/2, where /x is the reduced mass of the atoms forming the bond. 

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