The energies for an electron in the K, L, and M shells of...

The energies for an electron in the $K, L,$ and $M$ shells of the tungsten atom are -69,500 eV, -12,000 eV, and -2200 eV, respectively. Calculate the wavelengths of the $K_\alpha$ and $K_\beta$ x rays of tungsten.

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Key Concepts

Electronic Transitions

Electrons within atoms occupy discrete energy levels. When an electron transitions from a higher energy level to a lower one, the difference in energy between the two levels is emitted as a photon. This process underpins the production of x-ray emissions in atoms, where inner-shell electron transitions generate high-energy photons.

Characteristic X-rays

Characteristic x-rays are produced when an electron vacancy in an inner shell is filled by an electron coming from a higher energy shell. The resulting photon has an energy equal to the difference in binding energies between the two shells. For instance, the K? and K? x-rays are emitted due to electrons transitioning from higher shells (like L or M) to the K shell, and are unique to each element.

Energy-Wavelength Relationship

The relationship between the energy of a photon and its wavelength is given by the equation E = hc/?, where E is the energy, h is Planck's constant, and c is the speed of light. This fundamental relationship is used to calculate the wavelength of an emitted photon once the energy difference of the electron transition is known.

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