Atomic numbers of two elements are 31 and 41. Find the ratio of the wavelength of the  are

Ratio of Wavelength of K-alpha Lines

Ratio of Wavelengths of K_α Lines for Elements with Atomic Numbers 31 and 41

Moseley's Law for K_α lines states that the wavelength λ is inversely proportional to the square of (Z - 1), where Z is the atomic number:

λ ∝ 1 / (Z - 1)²

Given atomic numbers Z₁ = 31 and Z₂ = 41, the ratio of their wavelengths is:

Ratio = λ₁ / λ₂ = ((Z₂ - 1) / (Z₁ - 1))²

Substitute the values:

Ratio = ((41 - 1) / (31 - 1))² = (40 / 30)² = (4/3)² = 16 / 9

Final Answer

The ratio of the wavelengths of the K_α lines for the elements with atomic numbers 31 and 41 is 16:9.