`K_alpha` wavelength emitted by an atom of atomic number Z=11 is `lambda`. Find the atomic number for an atom that emits `K_alpha` radiation with wavelength `4lambda`.
(a) Z=6 (b) Z=4
(c ) Z=11 (d) Z=44.

Options

A. 4
B. 6
C. 11
D. 44

Answer

B

Explanation

the wavelength of `K_alpha` line emitted by an atom is given by
`lamda_(K_alpha) = (K')/(Z -1)^2` where K' is a constant
`therefore lamda_1 =(K')/(Z -1)^2 = (k') /(11-1)^2 = (k')/(100)`
Similarly, `lamda_2 = (K')/(Z'-1)^2`
`therefore lamda_2/lamda_1 = 4/1 = (100)/(Z '-1)^2`
`therefore (Z'-1)^2 = 25 therefore Z' - 1 = 5 therefore Z' = 6`