Aluminium ( Z = 13 ) and zinc ( Z = 30 ) emit K_ X-rays with wavelengths of 887 pm and 146 pm , respectively. Applying Moseley's law = a(Z - b) , determine the wavelength of the K_ X-ray emitted by iron ( Z = 26 ).

Step-by-step solution

According to Moseley's law, the frequency of the emitted X-ray is given by: = a(Z - b) Since = c , we can write this in terms of wavelength as: 1 = k(Z - b) where k = a c . This shows that 1 is a linear function of the atomic number Z . Given the data for Aluminium ( Z = 13 ) and Zinc ( Z = 30 ): 1 887 = k(13 - b) ... (i) 1 146 = k(30 - b) ... (ii) For Iron ( Z = 26 ), let the wavelength be _ Fe : 1 _ Fe = k(26 - b) ... (iii) Subtracting equation (i) from (ii) gives: k(30 - 13) = 1 146 - 1 887 17k 0.08276 - 0.03358