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  • In the Auger process, an atom makes a transition to a lower state without emitting a photon. The excess energy is transferred to an outer electron which may be ejected by the atom. (This is called an Auger electron). Assuming the nucleus to be massive, ca

In the Auger process, an atom makes a transition to a lower state without emitting a photon. The excess energy is transferred to an outer electron which may be ejected by the atom. (This is called an Auger electron). Assuming the nucleus to be massive, calculate the kinetic energy of an n = 4 Auger electron emitted by Chromium by absorbing the energy from a n = 2 to n = 1 transition.

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Explanation:-

Auger Effect: While responding to the downward transition by another electron in the atom, the characteristic energies of the atoms are ejected, and this process is called the Auger effect. The bombardment with the high-energy electrons results in the formation of a vacancy in Auger spectroscopy. But the effect is possible when other interaction leads to vacancy formation. It is an electron arrange method after the nucleus captures the electron.

During the removal of the electron shell from the atom, a simultaneous response by a higher-level electron will result in a downward transition and fill the vacancy. Multiple times there is a release of photons along with the vacancy filling, the energy of these photons is equal to the energy gap between the upper and lower levels.

This is also known as X-ray fluorescence due to the presence of all these heavy atoms in the x-ray region. But the same emission process for lighter atoms or outer electrons forms a line spectrum.

But in most cases, a higher-level electron fills the vacancy and emits a photon.

 

Because the nucleus is large and thus the momentum of the atom is neglected, and the complete transitional energy is transferred to the Auger electron. The energy states represented by Bohr’s model are similar to the states of Cr due to the presence of a single valance electron in its atom.

The energy of the nth state E_{n}=-Rch\frac{Z^{2}}{n^{2}}=-13.6\frac{Z^{2}}{n^{2}}eV where R is the Rydberg constant and Z=24

 

The energy released in a transition from 2 to 1 is

\Delta E=13.6Z^{2}\left ( \frac{1}{n_{1}^{2}}-\frac{1}{n_{2}^{2}} \right )=13.6Z^{2}\left ( \frac{1}{1^{2}}-\frac{1}{2^{2}} \right )

=13.6Z^{2}\left ( 1-\frac{1}{4} \right )=13.6Z^{2}\times \frac{3}{4}

The energy required by the Auger electron is

KE=13.6Z^{2}\left ( \frac{3}{4}-\frac{1}{16} \right )=5385.6eV

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