Revision: Dual Nature of Radiation and Matter >> Dual Nature of Radiation and Matter Physics (Theory) ISC (Science) ISC Class 12 CISCE

Statement

The frequency of a spectral line in the X-ray spectrum varies as the square of the atomic number of the element emitting it.

\[\sqrt ν\] = k(Z − b)

or

ν = constant (Z − b)2

where
Z = atomic number,
b = screening factor,
k = constant.

Proof / Explanation:

Moseley studied characteristic X-rays emitted by different elements used as targets in an X-ray tube and determined their frequencies.

He plotted a graph with:

• Atomic number Z on the x-axis

• Square root of frequency \[\sqrt ν\]​ on the y-axis

For Kα and Kβ lines, the graph was a straight line.

Thus,

\[\sqrt ν\] ∝ (Z − b)

or

ν ∝ (Z − b)²

For Kα line:

ν = \[\frac {1}{4}\]Rc(Z−1)²

This is similar to Bohr’s formula and shows that Kα radiation is produced by the transition of an electron from the L-shell (n = 2) to the K-shell (n = 1). The term (Z−1) appears because one electron is removed from the K-shell.

Conclusion:

The frequency of characteristic X-rays depends on the atomic number of the element.

Importance of Moseley’s Law:

1. It proved that atomic number, not atomic weight, determines the physical and chemical properties of elements.
2. It helped refine the periodic table.
3. It helped in the discovery of new elements such as hafnium, illinium, and rhenium.
4. It helped to determine the atomic numbers of rare-earth elements and fix their correct positions in the periodic table.