The de Broglie Picture of Gaseous Lithium Hydride
In one of our
previous communications {1}, we pointed out that there is a discrepancy in the
representation of the hydrogen molecule (H2) in chemistry and
physics textbooks and de Broglie's representation. Here we will consider the
picture of the gaseous LiH (hereinafter LiH) given in these textbooks and the
picture of the same molecule based on Broglie's theory of the wave nature of
matter (duality).
LiH is the
simplest neutral heteronuclear diatomic molecule gaseous at non-STP. The mass
of Li is about 1.2 × 10-26 medical history[1]
and the diameter of its nucleus (or Li3+) is about 10-14
m; the mass of the hydrogen atom (H) is about 1.7 × 10-27 kg
and the diameter of its nucleus (proton) is about 1.7 × 10-15 m.[2] The mass of LiH is
about 1.3 × 10-26 kg
and the experimental bond length of gaseous LiH is about 1.6 × 10-8 m {2}. Thus, the distance between Li (or its nucleus: Li3+) and H (or its nucleus: proton H+) in this molecule
is about 3 × 106 Li3+ diameters and about 107 H+ diameters.
According to the model of the above textbooks, LiH consists of two independent species: partly positive Li+δ and partly negative H-δ. They are linked by an ionic-covalent bond.[3] However, this picture does not just agree with the picture of this molecule based on de Broglie's hypothesis.
The de Broglie equation can be used to describe the wave nature of LiH in motion. Usually, this equation is expressed in the following form
λ = h/my ... (1).
where h (= 6.63 × 10-34 J sec) is Planck's constant, λ and m are the wavelength and the mass of a particle moving at a speed υ.
If LiH travels with a non-relativistic speed υ its wavelength is then
λ(LiH) = h/m(LiH)υ ... (2)
where m(LiH) is the mass of LiH. As the contribution of the mass of the electron(s) is negligible to the mass of Li and to the mass of H[4], we have
λ(Li) = h/m(Li3+)υ and λ(H) = h/m(H+)υ … (3).
As we noted above, the distance between Li and H is
equal to about 3 × 106 Li3+ diameters and to about 107 H+ diameters. Therefore, one could
hypothesize that LiH consists of completely separated Li+δ and H-δ interconnected by an ionic-covalent
bond and having independent wavelengths: λ(Li)
and λ(H) [see eqn. (3)]. Since m(Li3+) is about 8
times larger than m(H+) then, according to eqn. (3), λ(Li) ≈ 8λ(H).
As we noted above, the distance between Li and H is
equal to about 3 × 106 Li3+ diameters and to about 107 H+ diameters. Therefore, one could
hypothesize that LiH consists of completely separated Li+δ and H-δ interconnected by an ionic-covalent
bond and having independent wavelengths: λ(Li)
and λ(H) [see eqn. (3)]. Since m(Li3+) is about 8
times larger than m(H+) then, according to eqn. (3), λ(Li) ≈ 8λ(H).
As in the case
of H2 {1}, quantum mechanically speaking, the question arises: Can
the gas molecule LiH in motion be represented by one wave packet of this
molecule as a whole or by two separated wave packets of Li3+ and H+?
Fig. 1: Highly exaggerated
two-dimensional picture of the (dumbbell shape) partly “fused” nucleus of LiH.
This dilemma can be extended to all
diatomic heteronuclear molecules gaseous at STP (e.g. the carbon monoxide
molecule: CO) or non-STP (e. g. the cesium iodide molecule: CsI).
References
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