The wavelength of `K_(alpha)` X-ray line for an element is `0.42Å` . Find the wavelength of `K_(beta)` line emitted by the same element.

Explanation

The characterstic wavelength for particular element is
given by `(1)/(lambda)=R(Z-b)^(2)((1)/(n_(1)^(2))-(1)/(n_(2)^(2)))`
For `K_(alpha`)line
`(1)/(lambda_(alpha))=(Z-b)^(2)R((1)/(1^(2))-(1)/(n_(2)^(2)))=(Z-b)^(2)R((3)/(4))`
For `K_(beta)` line,
`(1)/(lambda)=(Z-b)^(2)((1)/(1^(2))-(1)/(3^(2)))=(Z-b)^(2)R((8)/(9))`
`rArr(lambda_(beta))/(lambda_(alpha))=((3//4))/((8//9))=(27)/(32)`
It is given that `lambda_(alpha)` is `0.42Å`
`:." " lambda_(beta)=0.42xx(27)/(32)=0.35Å`