Element A has atomic number 11 and its Kα wavelength is 1.20 nm. Another element B has Kα wavelength 0.300 nm. Assume the same K-series screening constant for both elements. Using Moseley's law, first determine the atomic number of B. Then use λ(Kβ) = (27 ÷ 32)λ(Kα) to predict the Kβ wavelength of element B. Which pair is correct?
Options

Question

Element A has atomic number 11 and its Kα wavelength is 1.20 nm. Another element B has Kα wavelength 0.300 nm. Assume the same K-series screening constant for both elements. Using Moseley's law, first determine the atomic number of B. Then use λ(Kβ) = (27 ÷ 32)λ(Kα) to predict the Kβ wavelength of element B. Which pair is correct?

Options

G1 Physics · Accepted Answer

Because λ(Kα) ∝ 1 ÷ (Z−1)², λ(A) ÷ λ(B) = (Z(B)−1)² ÷ (Z(A)−1)². Given, 1.20 ÷ 0.300 = 4. Also, Z(A)−1 = 11−1 = 10. Therefore, 4 = (Z(B)−1)² ÷ 100. Taking the positive square root: 2 = (Z(B)−1) ÷ 10. Thus, Z(B)−1 = 20, so Z(B) = 21. Now calculate the Kβ wavelength: λ(Kβ) = 0.300×27 ÷ 32 = 0.253125 nm ≈ 0.253 nm. Therefore the correct pair is Z(B) = 21 and λ(Kβ) ≈ 0.253 nm. Correct option: B.