How is Hamiltonian energy of orbital differ from orbital in certain

In summary, the Hamiltonian energy of the orbital in a certain atom differs from the orbital in another atom, even if they have the same number of electrons. This is because the atoms have different atomic numbers, resulting in different potential values in the Schrodinger equation and ultimately different Hamiltonian eigenstates. The change in atomic number can also affect the potential value.
  • #1
boodyx1
2
0
how is Hamiltonian energy of orbital differ from orbital in certain atom with another atom although the two orbital have the same no. of electrons...
ex...Hamiltonian energy differ in lithium and hydrogen although both have one electron in last orbital
please help me quickly
 
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  • #2


lol, just curious, why the rush? ;]

Well these 2 atoms you mention have nothing in common. They have different atomic number, which means the potential V (that gets in schrodinger equation) is different which finally means that you'll get different Hamiltonian eigenstates (energies)
 
  • #3


r u trust in this answer...and how the atomic no. can change in V
 

1. How is Hamiltonian energy of orbital determined?

The Hamiltonian energy of an orbital is determined by the quantum mechanical operator called the Hamiltonian, which represents the total energy of a system including the kinetic and potential energy of the particles in that system. The Hamiltonian energy of an orbital is dependent on the wave function of the orbital, which describes the probability of finding an electron in a particular location around the nucleus.

2. What is the difference between the Hamiltonian energy of an orbital and the orbital itself?

The Hamiltonian energy of an orbital is a mathematical representation of the total energy of an orbital, while the orbital itself is a physical region around the nucleus where there is a high probability of finding an electron. The Hamiltonian energy is a theoretical concept used in quantum mechanics, while the orbital is a real space where electrons can exist.

3. How does the Hamiltonian energy of an orbital relate to its energy level?

The Hamiltonian energy of an orbital is directly related to the energy level of the orbital. In quantum mechanics, each energy level corresponds to a specific set of quantum numbers, which determine the energy of the orbital. The higher the energy level, the higher the Hamiltonian energy of the orbital.

4. How does the Hamiltonian energy of an orbital differ from the energy of an electron in that orbital?

The Hamiltonian energy of an orbital is the total energy of the orbital, which includes the kinetic and potential energy of the electrons, while the energy of an electron in that orbital is the specific energy of that electron within the orbital. The energy of an electron is determined by its quantum numbers and is different for each electron in the same orbital.

5. Can the Hamiltonian energy of an orbital change?

Yes, the Hamiltonian energy of an orbital can change as electrons move within the orbital or as the external environment of the atom changes. The Hamiltonian energy is affected by factors such as the strength of the nucleus, the presence of other electrons, and the external electric and magnetic fields. These changes in the Hamiltonian energy can result in changes in the energy level and properties of the orbital.

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