The wavelength of the characteristic X - ray `k_(alpha )` line emitted by a hydrogens like element is `0.32 lambda ` . The wavelength of the `K_(beta)` line emitted by the same element will be …..

Explanation

`1/lambda=(Z-b)^(2)R(1/n_(1)^(2)-1/n_(2)^(2))`
For `K_(alpha):1/lambda_(alpha)=(Z-b)^(2)R(1/1^(2)-1/2^(2))`
`=(Z-b)^(2)R(3/4)`
`K_(beta):1/lambda_(beta)=(Z-b)^(2)R(1/1^(2)-1/3^(2))`
`=(Z-b)^(2)R(8/9)`
`lambda_(beta)/lambda_(alpha)=(3//4)/(8//9)=27/32`
`lambda_(beta)/0.32=27/32`
`lambda_(beta)=0.27 Å`