When the voltage applied to an X-ray tube increased from `V_(1)=15.5kV` to `V_(2)=31kV` the wavelength interval between the `K_(alpha)` line and the cut-off wavelength of te continuous X-ray spectrum increases by a factor of `1.3`. If te atomic number of the element of the target is z. Then the value of `(z)/(13)` will be: (take `hc=1240eVnm` and `R=1xx(10^(7))/(m))`

Answer

2

Explanation

`lamda_(th)=(hc)/(eV_(a))`
`(1)/(lamda_(Kalpha)))=R(z-1)^(2)((1)/(1^(2))-(1)/(2^(2)))`
`(13)/(10)(lamda_(K_(alpha))-lamda_(th))-(lamda_(Kalpha)-(lamda_(th))/(2))`
`(3)/(10)lamda_(K_(alpha))=((13)/(10)-(1)/(2))lamda_(th)`
`(3)/(10)((4xx10^(-7))/(3(z_(7))^(2))=((8)/(10))(12.4xx10^(-7))/(15.5xx10^(3))implies(5000)/(8)`
`=(z-1)^(2)`
`625=(z-1)^(2)impliesz=26`