The Kα, Lα, and Mα x rays are emitted in the n=2 →n=1, n=3 →n=2, and n=4 →n=3 transitions respec

step 1 So here we have four shells, K -shell, L -shell, M -shell, and N -shell here. And we need to fig

The Kα, Lα, and Mα x rays are emitted in the n=2 →n=1, n=3...

The $K_{\alpha}, L_{\alpha}$, and $M_{\alpha}$ x rays are emitted in the $n=2 \rightarrow n=1, n=3 \rightarrow n=2$, and $n=4 \rightarrow n=3$ transitions respectively. For calcium $(Z=20)$ the energies of these transitions are $3.69 \mathrm{keV}, 0.341 \mathrm{keV},$ and $0.024 \mathrm{keV},$ respectively. Suppose that energetic photons impinging on a calcium surface cause ejection of an electron from the $K$ shell of the surface atoms. Compute the energies of the Auger electrons that may be emitted from the $L, M,$ and $N$ shells $(n=2,3,$ and 4$)$ of the sample atoms, in addition to the characteristic X rays.

Key Concepts

Atomic Electron Transitions

This concept involves electrons moving between discrete energy levels within an atom. When an electron drops from a higher to a lower energy level, the energy difference is released in the form of a photon. This fundamental idea underlies many spectroscopic techniques and is the basis for the emission of characteristic radiation when inner-shell vacancies are filled.

Characteristic X-Ray Emission

Characteristic X-ray emission occurs when an inner-shell vacancy, created by electron ejection, is filled by an electron from a higher energy shell. The resulting photon has an energy that corresponds exactly to the difference between the two involved energy levels. The notation (such as K, L, M) refers to these principal energy shells and distinguishes different X-ray lines.

Auger Effect

The Auger effect is a non-radiative process that competes with X-ray emission. When an inner-shell electron is removed, an electron from a higher energy level may fill the vacancy and the excess energy is transferred to another electron instead of being emitted as a photon. This secondary ejected electron is the Auger electron, and its kinetic energy is determined by the binding energies of the electrons involved in the cascade process.

Energy Conservation in Atomic Relaxation Processes

Energy conservation is a critical principle in atomic relaxation processes, including both X-ray emission and the Auger effect. The energy difference between the initial and final states determines the energy of the emitted photon or the kinetic energy of the Auger electron. This concept is used to calculate the energies of both radiative and non-radiative transitions in atoms.

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