The wavelength of the first line of Lyman series for hydrogen atom is equal to that of the second line of Balmer series for a hydrogen-like ion. The atomic number `Z` of hydrogen-like ion is

Options

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

Answer

D

Explanation

for first line of Lyman series of hydrogen
`(hc )/(lamda_1)= R hc ((1)/(I^2 ) - (1)/( 2^2))`
for second line of balmer series of hydrogen like ion `(hc)/( lamda^2) = z^2 RhC ((1)/(I^2) - (1)/(2^2))`
for second line of balmer series of hydrogen like ion
`(hc )/ ( lamda_2) = z^2 rhc ((1)/(2^2)-(1)/(4^2))`
by question `lamda _1=lamda _2 implies ((1)/(1) -1/2) = z^2 (1/4 -1/16) or z=2`