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what_are_electrons
For a ground state Hydrogen atomic system (1 electron and 1 proton - not molecular di-hydrogen), what energies are being exerted by the proton to hold that electron? Does TE = KE + PE apply?
TE=KE+PE applies, but you cannot use classical mechanics to describe the hydrogen atom. Rather, you must use quantum mechanics; nonrelativistic (Schroedinger) will do nicely for this problem and gives that the binding energy is 13.6eV. The only interaction between electron and proton is assumed to be electrostatic (Coulomb) in this picture; one can add corrections to this for improved accuracy.what_are_electrons said:For a ground state Hydrogen atomic system (1 electron and 1 proton - not molecular di-hydrogen), what energies are being exerted by the proton to hold that electron? Does TE = KE + PE apply?
zefram_c said:TE=KE+PE applies, but you cannot use classical mechanics to describe the hydrogen atom. Rather, you must use quantum mechanics; nonrelativistic (Schroedinger) will do nicely for this problem and gives that the binding energy is 13.6eV. The only interaction between electron and proton is assumed to be electrostatic (Coulomb) in this picture; one can add corrections to this for improved accuracy.
Actually, no "force" prevents it. When one solves the Schroedinger equation, the requirement that physically acceptable solutions be normalizable results in discrete bound states (ie only some binding energies are permitted, the electron can be bound by 13.6eV or 3.4eV but nothing in between) for all attractive potentials that I know of. So a physical explanation would be that if you try to localize the electron in a small volume close to the nucleus, the resulting uncertainty in its momentum (and thence energy) eventually overcomes the Coulomb attraction and prevents further localization. The discrete bound states are a result of the mathematics.what_are_electrons said:Please refresh my memory about what force, QM based or CM based, prevents the electron cloud from touching the nucleus.
I suppose the best answer to that is "because it works" - experimentally, we find that the Maxwell equations work on any scale at which quantization of the EM field can be neglected.And, why is it that we can use Coulomb's Force equation, that was derived from a large macro-scale torsion balance, to describe the electrostatics (or EM fields) that exist between the electron and the proton of hydrogen.
The notation "H (1s) electron" refers to a hydrogen atom with one electron in its first energy level, or "1s" orbital. The "BE=13.6eV" indicates the binding energy of this electron, which is the amount of energy required to remove the electron from the atom.
The binding energy of an electron in an atom is determined by the energy levels of the atom's orbitals and the attractive force between the nucleus and the electron. In the case of the H (1s) electron, its binding energy is equal to the energy of the first energy level, which is 13.6 electron volts (eV) for a hydrogen atom.
The value of 13.6eV for the binding energy of the H (1s) electron is a fundamental constant in quantum mechanics known as the Rydberg constant. It is used to calculate the binding energies of electrons in other atoms and molecules, and is an important factor in understanding atomic structure and chemical bonding.
The nucleus, which contains the protons and neutrons of an atom, exerts a strong attractive force on the electrons orbiting it. This attraction is what keeps the electron in its energy level and determines its binding energy. In the case of the H (1s) electron, the attractive force from the single proton in the nucleus results in the binding energy of 13.6eV.
Yes, the binding energy of an electron can change if the atom undergoes a chemical reaction or is exposed to external energy. For example, if a hydrogen atom gains or loses an electron, the binding energy of the remaining electron in the atom will change. Additionally, if the atom is exposed to high energy radiation, such as x-rays, the electron's binding energy can increase or decrease depending on the intensity of the radiation.