Moseley’s law | Atomic and Molecular physics

Moseley’s law

According to it, the frequency of a spectral line in X-ray spectrum varies as the square of the atomic number of the element emitting it.
If 𝜈 is the frequency of spectral line in X-ray spectra and Z is the atomic number of element, then
𝜈 = Z² ⇒ √𝜈 ∝ Z
or √𝜈 = a (Z– b)
Here (Z –b) is the effective atomic number of emitting element and b is the characteristic constant or screening constant.

Importance of Moseley’s law

The characteristic property of an element depends on their atomic number, not on their masses.
So the position of some elements in periodic table was rearranged.
On the basis of Moseley law some new elements of periodic table was discovered like Hf (72), In (61), Re (75) etc.

Explanation of Moseley’s law on the basis of Bohr’s theory

The energy of electron in n₁ and n₂ orbits are given by

Since the positive nucleus is screened by rest of the electrons.
Therefore we use atomic number (Z– b) in place of Z.

If Z is very large, b₁ ≈ b₂ ≈ b

For K_α line, n₁ = 2 and n₂ = 1

For K_α line, a = 3Rc/4 and b = 1
Here R is Rydberg’s constant, and c is velocity of light.

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