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The ground state of a quantum-mechanical system is its stationary state of lowest energy; the energy of the ground state is known as the zero-point energy of the system. An excited state is any state with energy greater than the ground state. In quantum field theory, the ground state is usually called the vacuum state or the vacuum. If more ...
The Madelung energy ordering rule applies only to neutral atoms in their ground state. There are twenty elements (eleven in the d-block and nine in the f-block) for which the Madelung rule predicts an electron configuration that differs from that determined experimentally, although the Madelung-predicted electron configurations are at least ...
In these terms, an example of zero-point energy is the above E = ħω / 2 associated with the ground state of the quantum harmonic oscillator. In quantum mechanical terms, the zero-point energy is the expectation value of the Hamiltonian of the system in the ground state. If more than one ground state exists, they are said to be ...
As an example, the ground state configuration of the sodium atom is 1s 2 2s 2 2p 6 3s 1, as deduced from the Aufbau principle (see below). The first excited state is obtained by promoting a 3s electron to the 3p subshell, to obtain the 1s 2 2s 2 2p 6 3p 1 configuration, abbreviated as the 3p level.
Gaseous chromium has a ground-state electron configuration of 3d 5 4s 1. It is the first element in the periodic table whose configuration violates the Aufbau principle . Exceptions to the principle also occur later in the periodic table for elements such as copper , niobium and molybdenum .
Atoms can be excited by heat, electricity, or light. The hydrogen atom provides a simple example of this concept.. The ground state of the hydrogen atom has the atom's single electron in the lowest possible orbital (that is, the spherically symmetric "1s" wave function, which, so far, has been demonstrated to have the lowest possible quantum numbers).
The potential is a Coulomb interaction, so the corresponding individual electron energies are given by = = and the corresponding spatial wave function is given by (,) = (+) If Z e was 1.70, that would make the expression above for the ground state energy agree with the experimental value E 0 = −2.903 a.u. of the ground state energy of helium.
The lightest atom that requires the second rule to determine the ground state term is titanium (Ti, Z = 22) with electron configuration 1s 2 2s 2 2p 6 3s 2 3p 6 3d 2 4s 2. In this case the open shell is 3d 2 and the allowed terms include three singlets ( 1 S, 1 D, and 1 G) and two triplets ( 3 P and 3 F).