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

We know,
` E_1 for H =- 13 . 6 eV`
` E-2` for ` H =-( 9 13. 6 )/( 2^2) =- ( 13 . 6)/4 =- 2 3.4 eV`
` :. E_2 - e_1 =- 3.4 - (- 13 . 6 ) = + 10 . 2 eV`
`:.` Difference in two levels ` = 10. 2 eV`
Also for transition of H-like atom
` lambda = 3.0 xx 10^(-8) m` ltbr gt `:. 1/( lambda) = R_H xx Z^2 [ 2/1^2 - 1/2^2]`
` :. 1/( 3 xx 10^8) = 1009677 xx 10^2 xx Z^2 [3/4]`
` [:. R_H = 109677 cms^(-1) = 109677 xx 10^2 m^(-1) ]`
` :. Z^2 = 4 :. Z=2`
H-like atom is `He ^+.`