Question

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.

Answer 1

Auger Effect: The Auger effect is a process by which electrons with characteristic energies are ejected from atoms in response to a downward transition by another electron in the atom. In Auger spectroscopy, the vacancy is produced by bombardment with high-energy electrons, but the Auger effect can occur if the vacancy is produced by other interactions. It is observed as one of the methods of electron rearrangement after electron capture into the nucleus.

If an inner shell electron is removed from an atom, an electron from a higher level will quickly make the transition downward to fill the vacancy. Sometimes this transition will be accompanied by an emitted photon whose quantum energy matches the energy gap between the upper and lower level. Since for heavy atoms this quantum energy will be in the x-ray region, it is commonly called x.-ray fluorescence. This emission process for lighter atoms and outer electrons gives rise to line spectra.

In other cases, the energy released by the downward transition is given to one of the outer electrons instead of to a photon, and this electron is then ejected from the atom with an energy equal to. the energy lost by the electron which made the downward transition minus the binding energy of the electron that is ejected from the atom. Though more involved in interpretation than optical spectra, the analysis of the energy spectrum of these emitted electrons does give information about dying atomic energy levels. The Auger effect bears some resemblance to the internal conversion of the nucleus, which also ejects an electron.

Sometimes an upper election drops to fill the vacancy, emitting a photon.

As the nucleus is massive, the recoil momentum of the atom may be neglected and the entire energy of the transition may be considered transferred to the Auger electron. As there is a single valence electron in Cr, the energy states may be thought of as given by the Bohr model.

The energy E_n of the n^th state

`E_n = + Z^2 R[1/n_1^2 - 1/n_2^2]`

= `Z^2 R [1/1 - 1/4]` .....[For n₁ = 1, n₂ = 2]

Z = 24

R = Rydberg constant

∴ `E_n = 3/4 Z^2 R`

The energy required to eject an electron from n = 4 state is `E_4 = Z^2 R 1/4^2 = 1/16 Z^2 R`

The energy given to electron is converted into KE. of the ejected electron.

Hence, the KE. of Auger (ejected) electron = E_n – E₄ 

K.E. = `Z^2R 3/4 - 1/16 Z^2R`

= `11/16 Z^2R`

= `11/16 xx 24 xx 24 xx 13.6` eV

K.E. = 11 × 36 × 13.6  = 5385.6 eV