The wavelength of kα, X-rays produced by an X-ray tube 0.76Å. The atomic number of the anode material of the tube is

Options

(a) 20
(b) 60
(c) 41
(d) 80

Correct Answer:

41

Explanation:

Given, wavelength, λ(kα) = 0.76 Å = 0.76 × 10⁻¹° m
Moseley’s empirical formula for Kα X-rays when adapted to Bohr model is given by,
hʋ(Kα) = (3/4) × 13.6 (Z-1)² eV
hc/λ(kα) = (3/4) × 13.6 × 1.6 × 10⁻¹⁹ (Z-1)² J
[Since, 1 eV = 1.6 × 10⁻¹⁹ J]
We know that, h = 6.626 × 10⁻³⁴ J-s and c = 3 × 10⁸ ms⁻¹
Substituting the values in the above equations, we get
(6.626 × 10⁻³⁴ × 3 × 10⁸)/(0.76 × 10⁻¹°) = 16.08 × 10⁻¹⁹ (Z-1)²
26.15 × 10⁻¹⁶ = 16.03 × 10⁻¹⁹ (Z-1)²
1.63 × 10³ = (Z-1)² ⇒ 16.3 × 10² = (Z-1)²
⇒ Z – 1 = 40.4 ⇒ Z = 40.4 + 1 ≈ 4.1