When the voltage applied to an X-ray tube increased from `V_(1)15.5` KV to `V_(2)` = 31 KV, the wavelength interval between the `K_(alpha)` line and the short wavelength cut-off of the continuous X-ray spectrum increases by a factor of 1.3. If the atomic number of the element of the target is 13N, where N is an integer find N (Take : hc = 1240 eV and R=`1xx10^(7)//m`)

Answer

`0002`

Explanation

`lambda_(th)=(hc)/(eV_(a))`
`(1)/(lambda_(K alpha))=R(z-1)^(2)((1)/(1^(2))-(1)/(2^(2)))`
`(143)/(10)(lambda_(K alpha)-lambda_(th))=(lambda_(Kalpha)-(lambda_(th))/(2))`
`(3)/(10)lambda_(K alpha)=((13)/(10)-(1)/(2))lambda_(th)`
`(3)/(10)((4xx10^(-7))/(3(z_(7))^(2)))=((8)/(10))(12.4xx10^(-7))/(15.5xx10^(3))rArr(5000)/(8)=(z-1)^(2)`
`625=(z-1)^(2) " " rArr z = 26`