Intriguing Peculiarities of the Hydrogen and Lithium Hydride Molecules
Including the Entanglement
Laboratory for Geochemistry,
Cosmochemistry&Astrochemistry,
University of Niš, pavleipremovic@yahoo.com, Niš, Serbia
In the first part of this communication, we will consider the homopolar diatomic hydrogen molecule (H2) and in the second part the heteronuclear diatomic lithium hydride molecule (LiH). De Broglie’s equation can be used to describe the wave nature of a particle in motion
λ = h/mυ ... (1).
where h (= 6.63 × 10-34
J sec)[1] is
Planck's constant, λ and m are the wavelength and the mass of a particle
moving at a speed υ. For the sake of simplicity, we will consider H2 and LiH are moving at a non-relativistic speed υ.
We also want to remind you here that, by definition, two particles are
entangled when any change in one particle causes a change in the other no
matter how far apart, they are.
The first peculiarity.
H2 exists in two nuclear
isomeric forms: ortho H2 with the parallel proton’s spins (a triplet state) and para H2
with antiparallel spins (a single state). Ortho isomer is less stable than para
one but at STP., due to thermal excitation, the ratio of these isomers is 3:1 (ortho H2: para H2).
The experimental equilibrium bond length of H2 is about 7.4 ×
10-11 m or about 43500
diameters of the proton (its diameter is approximately 1.7 × 10-15 m). This is the
distance between two protons of H2. These
protons are spin-coupled though they are vastly apart in terms of their diameter. This
implies that they are entangled sharing two quantum states. Moreover, the two
electrons of H2 are also spin-coupled forming the spin-singlet ground
state (total spin is zero). This coupling also occurs at this huge distance. Therefore,
it implies that these electrons are also entangled.
The second peculiarity. Premović {1} calculated the most probable/average speed of H2 occupying 22.1 dm3 at STP is about 1500 m sec-1.[1] Employing eqn. (1) and the mass of H2 [ m (H2) = 3. 4 × 10-27 kg], he estimated that de Broglie’s average wavelength is approximately 1.3 ×10-10 m. Since the proton (hereinafter H+) is a component of H2 its most probable/ average speed would be also about 1500 m sec-1. Using the same equation, he estimated that de Broglie’s average wavelength of H+ is about 0.65 × 10-10 m. However, now the following questions arise: does a quantum mechanical model of H2 in non-relativistic motion consist of a single wave packet (with an “average de Broglie wavelength” of about 1.3 ×10-10 m) or does it consist of two vastly separated identical H+ wave packets (with an “average de Broglie wavelength” of about 0.65 × 10-10 m)? If de Broglie’s model is right, then the wave packets of these protons interact with each other giving the single wave packet. But now this wave packet should have the H+ an “average wavelength” of about 0.65 × 10-10 m but not about 1.3 ×10-10 m as the above single wave packet based on de Broglie’s approach. Moreover, if these two H wave packets interact with each other then they must be entangled since the distance between them is enormous: 43500 H+ diameters.
The third peculiarity. In one of our previous communications {2}, we proposed that Broglie’s waves of the protons of H2 interact
with each other. The
superposition of these waves can result in two types of interference depending
on whether their waves
are in phase or out of phase: constructive or destructive interference. As the distance
between the H2 protons is so large the superposition is possible
only if these two protons are entangled.
In their constructive interference, the resultant wave would have twice large the H+ amplitude but its wavelength would be the same as the H+ wavelength. Now we would deal with a single H2 wave packet. In the destructive interference, the two H+ waves would cancel each other so there would be no resultant wave. Does this mean there would be no H2 wave packet in this case?
The
peculiarities of LiH.
LiH consists of two independent species: partly positive Li+δ and
partly negative H-δ. They are linked by an ionic-covalent bond.[1] The diameter of its nucleus Li3+ (hereinafter Li3+)
is about 10-14 m and the diameter of its H+
nucleus is approximately 1.7 × 10-15 m; the
experimental bond length of gaseous LiH is about 1.6 × 10-8 m. Thus, the distance between Li (or Li3+) and
H (or H+) in this molecule is about 3 × 106
Li3+ diameters
and about 107 H+ diameters.
Let us assume that the de Broglie’s Li3+ wave of LiH interacts with its de Broglie’s H+ wave. The (constructive or destructive) superposition
of these dissimilar waves can result in rather complex two but
quite different de Broglie’s waves and the wave packets. As the bond length of
LiH is so large in terms of the Li3+ diameter or the H+ diameter then their superposition is possible only if the Li3+ and H+ nuclei are entangled.
However, now the following question arises: does a quantum mechanical model of LiH in non-relativistic motion consist of a single wave packet or does it consist of two vastly separated Li3+ and H+ wave packets? If de Broglie’s model is right, then the wave packets of these nuclei interact with each other giving the above single wave packet. But now this packet should be rather complicated. Moreover, if these two packets interact with each other then they have to be entangled since the distance between them is immense: about 3 × 106 Li3+ diameters and about 107 H+ diameters.
References
{2} P. I. Premović, The hydrogen molecule and deuterium atom in the light of de Broglie’s theory. The General Science Journal, May 2023. For the sake of clarity, I have modified the first part of a previous version of this communication which refers to de Broglie’s model of H2.
.jpg)
No comments:
Post a Comment