Estimate the difference in energy between the first and second Bohr's orbit for a hydrogen atom. At what minimum atomic number , a transition from `n = 2` to `n = 1` energy level would result in the emission of X -rays with `lambda = 3.0 xx 10^(-8) m`? Which hydogen -like species does this atomic number correspond to ?

Explanation

(a) We know that
`(1)/(lambda)=R_(H)Z^(2)[(1)/(n_(1)^(2))-(1)/(n_(2)^(2))] " Also " lambda =(hc)/(DeltaE) or (1)/(lambda)=(DeltaE)/(hc)`
`:. " " (DeltaE)/(hc)=R_(H)Z^(2) [(1)/(n_(1)^(2))-(1)/(n_(2)^(2))] or DeltaE =hc xxR_(H)Z^(2)[(1)/(n_(1)^(2))-(1)/(n_(2)^(2))]`
`DeltaE=(6.626xx10^(-34)Js)xx(3xx10^(8)ms^(-1))xx(1.09677xx10^(7)m^(-1))xx1[(1)/(1^(2))-(1)/(2^(2))]`
`=1.635xx10^(-18)J`
(b) Also `(1)/(lambda)=(DeltaE)/(hc)=R_(H)Z^(2)[(1)/(n_(1)^(2)-(1)/(n_(2)^(2))]`
`(1)/((3.0xx10^(-8)m))=(1.09677xx10^(7)m^(-1))Z^(2)[(1)/(1^(2))-(1)/(2^(2))]`
`Z^(2)=(1)/((3.0xxx10^(8)m))xx(4)/(3)xx(1)/(1.9677xx10^(7)m^(-1))=4.0523`
`Z=(4.0523)^(1//2)=2.013~~2`.