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A quantum number beginning in n = 3,ℓ = 0, describes an electron in the s orbital of the third electron shell of an atom. In chemistry, this quantum number is very important, since it specifies the shape of an atomic orbital and strongly influences chemical bonds and bond angles. The azimuthal quantum number can also denote the number of ...
These four numbers specify the unique and complete quantum state of any single electron in the atom, and they combine to compose the electron's wavefunction, or orbital. When solving to obtain the wave function, the Schrödinger equation resolves into three equations that lead to the first three quantum numbers, meaning that the three equations ...
The principal quantum number is one of four quantum numbers assigned to each electron in an atom to describe the quantum state of the electron. The other quantum numbers for bound electrons are the total angular momentum of the orbit ℓ, the angular momentum in the z direction ℓ z, and the spin of the electron s.
Uranium (chosen arbitrarily) has a high number of electrons; this diagram shows how they are arranged. :b An electron shell is a group of atomic orbitals with the same value of the principal quantum number n. Electron shells are made up of one or more electron subshells, or sublevels, which have two or more orbitals with the same angular ...
The magnetic quantum number determines the energy shift of an atomic orbital due to an external magnetic field (the Zeeman effect) — hence the name magnetic quantum number. However, the actual magnetic dipole moment of an electron in an atomic orbital arises not only from the electron angular momentum but also from the electron spin ...
is the number operator. When acting on a quantum mechanical photon number state, it returns the number of photons in mode (k, μ). This also holds when the number of photons in this mode is zero, then the number operator returns zero. To show the action of the number operator on a one-photon ket, we consider
Electron in the initial state is represented by a solid line, with an arrow indicating the spin of the particle e.g. pointing toward the vertex (→•). Electron in the final state is represented by a line, with an arrow indicating the spin of the particle e.g. pointing away from the vertex: (•→).
Each is therefore an unpaired electron, but the total spin is zero and the multiplicity is 2S + 1 = 1 despite the two unpaired electrons. The multiplicity of the second excited state is therefore not equal to the number of its unpaired electrons plus one, and the rule which is usually true for ground states is invalid for this excited state.