A piece of tissue paper soaked in polluted water is irradiated with continuous X-rays. The incident X-rays knock electrons out of the inner shells of the sample's atoms, causing excitation. Subsequently, characteristic X-rays are emitted. These emitted X-rays are then analysed, and their intensity is plotted as a function of wavelength (in the figure). Given that only K_ intensities are detected, identify the element

Step-by-step solution

Using Moseley's equation given in the problem: = (25 10¹⁴ Hz )(Z - 1)^2 We know the relation between frequency and wavelength is = c , where c = 3 10^8 m/s . Substituting into the equation and converting from pm to meters ( 10⁻¹² m ): 3 10^8 10⁻¹² = 25 10¹⁴ (Z - 1)^2 Rearranging to solve for (Z - 1)^2 : (Z - 1)^2 = 3 10²⁰ 25 10¹⁴ = 120000 Z = 1 + 120000 Now, we calculate the atomic number Z for each peak wavelength from the given graph: For = 78.9 pm : Z = 1 + 120000 78.9 1 + 39.0 = 40 Zr (Zirconium) For = 146 pm :