The Kα wavelength of an unknown element is 0.304 nm. Use the simplified Moseley relation 1 ÷ λ = (3 ÷ 4)R(Z−1)² with R = 1.097×10⁷ m⁻¹. Find the atomic number Z to the nearest integer.
Physics · Atomic Structure and X-rays · x-rays and its types
JEE Mains NEET JEE Advanced

Question

The Kα wavelength of an unknown element is 0.304 nm. Use the simplified Moseley relation 1 ÷ λ = (3 ÷ 4)R(Z−1)² with R = 1.097×10⁷ m⁻¹. Find the atomic number Z to the nearest integer.

G1 Physics · Accepted Answer

Convert wavelength to metres: λ = 0.304×10⁻⁹ m. Moseley's relation is 1 ÷ λ = (3 ÷ 4)R(Z−1)². Therefore, (Z−1)² = [1 ÷ λ] ÷ [(3 ÷ 4)R]. Substituting the values gives (Z−1)² ≈ 399.8. Hence, Z−1 ≈ √399.8 ≈ 20.0. Therefore, Z ≈ 21. Nearest integer: 21.