1.

The wavelength of the spectral live the Balner series of hydrogen atom is `6561 A^(@)` . The wavelength of the second spectralline in the Balmer series of singly - ionized belium atom isA. `1215 A^(2) `B. `1640 A^(2) `C. `2430 A^(2) `D. `4687 A^(2) `

Answer» Correct Answer - A
we know that `(1)/(lambda) = RZ^(2) [(1)/(n_(1)^(2)) - (1)./(n_(2)^(2))]
The wave length of spectal line in the balmar series of hydrogen atom is `6561Å` Here n_(2) = 3 and n_(1) = 2 `
` :. (1)/(6561) = R(1)^(2) ((1)/(4) - (1)/(9)) = (5R)/(36) ` ....(i)
For the second spectral line is the balmer of singly ionised belium ion `n_(2) = 4 and n_(1) = 2 , Z = 2 `
`:. (1)/(lambda) = R(2)^(2) [(1)/(4) - (1)/(16)] = (3R)/(4) `....(ii)
Dividingh equation (i) and equqtion (ii() we get
`(lambda)./(6561) = (5R)/(36) xx (4)/(3R) = (5)/(27)`
` :,. lambda= 1215 Å`


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