The wavelength of the K_ characteristic X-ray line emitted by an element with atomic number Z=11 is . If the wavelength of the K_ line emitted by an unknown element X is 4 , then the atomic number of element X is:

Step-by-step solution

According to Moseley's Law: = a(Z - b) For K_ lines, the screening constant b = 1 . Since frequency = c , we have: c (Z - 1) 1 (Z - 1) For the first element ( Z₁ = 11 ): 1 (11 - 1) = 10 For the unknown element X ( Z₂ ): 1 4 (Z₂ - 1) 2 (Z₂ - 1) Taking the ratio of the two equations: 2 1 = Z₂ - 1 10 2 = Z₂ - 1 10 Z₂ - 1 = 20 Z₂ = 21 Answer: 21