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

As is known, `K_(alpha)` line is emitted when an electron jumps to 1st stationary orbit form 2nd stationary orbit.
The frequency of `K_(alpha)` line is
`v_(alpha)=(me^4z^2)/(8in_0^2h^2)(1/(1^2)-1/(2^2))=K(3//4)... (i)`
where `K=(me^4z^2)/(8epsilon_0^2h^2)`
Now, `K_(beta)` line is emitted when an electron jumps to 1st stationary orbit form third sationary orbit
`:.` Frequency of `K_(beta)` line is
`v_(beta)=K(1/(1^2)-1/(3^2))=K(8//9)..... (ii)`
Dividing (i) by (ii), we get
`(v_(alpha))/(v_(beta))=(K(3//4))/(K(8//9))=3/4xx9/8=27/32`
As `lambda prop1/v :. (lambda_(beta))/(lambda_(alpha))=(v_(alpha))/(v_(beta))=27/32`
`lambda_(beta)=27/32 lambda_(alpha)=27/32xx0.32Å=0.27Å`