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

For hydrogen-like element
`(1)/(lambda) = Z^(2) R ((1)/(n_(1)^(2)) - (1)/(n_(2)^(2)))`
For `K_(alpha) line, (1)/(lambda) = Z^(2) R ((1)/(1^(2)) - (1)/(2^(2)))`
For `K_(beta) line, (1)/(lambda_(beta)) = Z^(2) R ((1)/(1^(2)) - (1)/(3^(2)))`
Driving, `(lambda_(beta))/(lambda_(alpha)) = (1^(1/2) - 2^(1/2))/(1^(1/2) - 3^(1/2)) = (1 - (1)/(4))/(1 - (1)/(9)) = (3//4)/(4 xx 8) = (3 xx 9)/(4 xx 8) = (27)/(32)`
`:. lambda_(beta) = (27)/(32) lambda_(alpha) = (27)/(32) xx 0.32 Å = 0.27 Å`