If the series limit of Lyman series for Hydrogen atom is equal to the series limit Balmer series for a hydorgen like atom, then atomic number of this hydrogen-like atom will be

Options

A. `1`
B. `2`
C. `3`
D. `4`

Answer

B

Explanation

By using `(1)/(lambda) = RZ^(2) [(1)/(n_(1)^(2))-(1)/(n_(2)^(2))]`
For Hydrogen atom `(1)/((lambda_(min))_(H)) = R [(1)/(1^(2))-(1)/(oo)] = R`
`rArr(lambda_(min)_(H)) = (1)/(R ) …….(i)`
For hydrogen-like atom `((1)/(lambda_(min)))_("atom") = RZ^(2)((1)/(2^(2))-(1)/(oo))`
`rArr (lambda_(min))_("atom") = (4)/(RZ^(2)) .....(ii)`
From equation (i) and (ii) `(1)/(R ) = (4)/(RZ^(2)) rArr Z = 2`.