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 ?

Answer

`10.2eV,Z=2`

Explanation

(i) `E_(E_(2)rarrn_(1))=13.6xxZ^(2)[(1)/(n_(1)^(2))-(1)/n_(2)^(2)]=13.6[1]^(2)[(1)/(1)-(1)/(4)]`
`=13.1xx1xx(3)/(4)=10.22eV`
(ii) `(1)/(lambda)=R_(H)Z^(2)[(1)/(n_(1)^(2))-(1)/n_(2)^(2)]`
`(1)/(3xx10^(-8))=1.09xx10^(7)xxZ^(2)[(1)/(4)-(1)/(1)]`
`(10^(8))/(3xx10^(7)xx1.09)=Z^(2)x(x-3)/(4)`
`(10xx4)/(3xx1.09x-3)=Z^(2)" "Z^(2)=-4" "Z=2`