Estimate the difference in energy between 1st and 2nd Bohr orbits for 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 xx 10^(-8) m? ` Which hydrogen atom 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`