It\'s very difficult to exactly calculate many of the properties of atoms heavie

Question

It's very difficult to exactly calculate many of the properties of atoms heavier than hydrogen, since

heavier atoms have both more particles in their nuclei, and more electrons bound to them, making for

very complex internal interactions affecting the energy level structure.

However, a simplified model of heavier atoms does allow us to roughly predict the energies and

wavelengths of their characteristic x-rays. These x-rays are emitted after an electron is knocked out of

one shell, and an electron from a higher energy level makes a downward transition to replace the

missing electron, emitting an x-ray in the process.

In the simplified model, we assume that, from the point of view of any electron, the atomic nucleus has

an effective charge Zeff that's smaller than the actual nuclear charge Z because one or more negatively

charged electrons “screen†some of the positive nuclear charge. The energies of electrons in each shell

are then calculated using the Bohr model for hydrogen-like atoms, with Zeff for that shell replacing Z.

• For either of the two electrons in a filled K shell: Zeff = Z – 1

â—¦ this is used to find the energy of an electron after it reaches and fills an empty K shell “slotâ€

• For an L-shell electron* if there is only one electron in the K shell: Zeff = Z – 3

• For an M-shell electron if there is only one electron in the K shell: Zeff = Z – 9

Question

Consider the characteristic Kβ line, which is produced when electrons drop from the M shell to an

empty state in the K shell. In the laboratory, a certain element's Kβ line is found at a wavelength of

20.234 pm. On the basis of this simplified model, which element would you expect this to be?

Explanation / Answer

z=3 i.e.lithium

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