Bohr atom
Original post
by carleto1234testing
Reply 1
Einstein's photon energy equation E = mc2 is physically invalid. The absorption of a photon by a body was said to increase the mass (Eo/c2) of an object; consequently, Einstein inertial mass (Eo/c2) is zero (m=0). The energy-momentum equivalence E2 = (mc2)2 + (pc)2, photon zero rest mass (m = 0), and Compton's photon momentum (p = h/λ) are used to form E = pc = hc/λ = hv but the energy-momentum does not change the fact that the absorbed photon does not increase the mass of the object which invalidates E = mc2.
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(edited 3 weeks ago)
Reply 2
12
Original post
by carleto1234How can electrons, which repel each other due to their like charges, still form stable structures within an atom?
Ciao,
Sandro
Reply 3
How can positively charged protons exist with the infinitesimal volume of a nuclear.
Reply 4
12
Original post
by carleto1234How can positively charged protons exist with the infinitesimal volume of a nuclear.
Ciao,
Sandro
Reply 5
What is the proton-proton net strong force for 1 ml of helium gas?
Reply 6
The particle-in-box normalization originates from the Bohr atom. Applying a spherical coordinate system on Schrodinger's box normalization is invalid. The box normalization procedure represents a structural transformation and is expressed in the spherical coordinate system to derive the equations of atomic orbitals; however, a spherical coordinate system requires a well-defined origin. In the particle-in-a-box normalization, no such origin exists. The electron in the original Bohr atom orbits alone the outer circumference of the atom. Consequently, the electromagnetic wave within the box is intended to mimic the electron orbiting the Bohr atom. Using a spherical coordinate system effectively imposes an origin at the center of the atom, which reverts back to the Bohr atom where the center of the atom is the nucleus. Using an analogy, consider a vibrating string forming a circle: the string has no beginning or end which is used to representing Schrodinger's continuous electromagnetic wave orbiting a nucleus. In the box normalization, the circular string is conceptually flattened into a straight line. Under these conditions, the oscillating string can be represented in a rectangular coordinate system but applying a spherical coordinate system to the flattened string introduces a logical inconsistency.
Schrodinger wave equation represented in a spherical coordinate system is invalid. Schrodinger’s wave equation (equ 66) is used to derive the equations of the atomic orbitals but the original plane wave of Schrodinger’s wave function (equ 70) is incompatible with a spherical coordinate system since the maximum amplitude of a plane wave is constant yet a spherical wave's maximum amplitude decreases as the distance from the origin increases; consequently, a plane wave is decomposed into spherical waves, and this is a standard, exact technique in quantum mechanics. What can happen is a plane wave can be mathematically represented as a sum of spherical waves for analysis in spherical coordinates. That’s a decomposition, not a physical transformation. The plane wave itself remains a plane wave; it doesn’t physically become a spherical longitudinal wave. Spherical waves that maximum amplitude decreases cannot decompose into a plane wave that has a constant maximum amplitude. Schrodinger's wave equation is based on a box normalization which is a structural transformation; therefore, Schrodinger's normalized wave equation, in spherical coordinate system,, cannot be used to derive equations that represent the structure of an atom (atomic orbitals). In addition, the atomic orbitals are derived using probability waves. Schrodinger does not use probability waves in his 1926 paper. The later addition of the probability waves to Schrodinger's wave equation was used to derive the structural equations of the atomic orbitals but a probability wave is nothing (uncertainty). Nothing cannot be used to derive equations that represent the structure of an atom.
Schrodinger wave equation represented in a spherical coordinate system is invalid. Schrodinger’s wave equation (equ 66) is used to derive the equations of the atomic orbitals but the original plane wave of Schrodinger’s wave function (equ 70) is incompatible with a spherical coordinate system since the maximum amplitude of a plane wave is constant yet a spherical wave's maximum amplitude decreases as the distance from the origin increases; consequently, a plane wave is decomposed into spherical waves, and this is a standard, exact technique in quantum mechanics. What can happen is a plane wave can be mathematically represented as a sum of spherical waves for analysis in spherical coordinates. That’s a decomposition, not a physical transformation. The plane wave itself remains a plane wave; it doesn’t physically become a spherical longitudinal wave. Spherical waves that maximum amplitude decreases cannot decompose into a plane wave that has a constant maximum amplitude. Schrodinger's wave equation is based on a box normalization which is a structural transformation; therefore, Schrodinger's normalized wave equation, in spherical coordinate system,, cannot be used to derive equations that represent the structure of an atom (atomic orbitals). In addition, the atomic orbitals are derived using probability waves. Schrodinger does not use probability waves in his 1926 paper. The later addition of the probability waves to Schrodinger's wave equation was used to derive the structural equations of the atomic orbitals but a probability wave is nothing (uncertainty). Nothing cannot be used to derive equations that represent the structure of an atom.
Reply 7
It might be worth noting which parts of your posts are copy and pasted from elsewhere, and which parts are your own statements/questions.
Reply 8
I saw this on Wiki sandbox
Reply 9
Original post
by carleto1234How can electrons, which repel each other due to their like charges, still form stable structures within an atom?
The spins on the electrons are opposite. In an orbital there can be a max of 2 electrons, with opposite spins. If they had the same spins, they wont be able to form stable structures. Smthing to do with the Pauli exclusion spin principle. Also, they are forced into different orbitals, so the repulsion between them is reduced.
Not too sure if this is correct, but was taught this in schl:>.
Reply 10
12
Original post
by CelestialMDThe spins on the electrons are opposite. In an orbital there can be a max of 2 electrons, with opposite spins. If they had the same spins, they wont be able to form stable structures. Smthing to do with the Pauli exclusion spin principle. Also, they are forced into different orbitals, so the repulsion between them is reduced.
Not too sure if this is correct, but was taught this in schl:>.
Not too sure if this is correct, but was taught this in schl:>.
An atom's stability? It's a mix of the Pauli exclusion principle, how electrons push each other away (Coulomb repulsion), and this thing called exchange energy. Pairing electrons with opposite spins is just one way to play by Pauli's rules. Often, if you've got electrons with the same spin chilling in their own orbitals, you get some extra stability from that exchange thing.
Ciao,
Sandro
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