Question

Which transition in hydrogen atomic spectrum will have the same wavelength as the transition, n = 4 to n = 2 energy level of he+ spectrum?

Answer 1

HEYA
I WILL DENOTE LAMBDA WITH L

for he+ ion  wave no.  = 1/L  = RZ²(1/n1²-1/n2²)
 
plug these values in it 
n1 = 2 
n2 = 4 
z = 2 (atomic no. of he)

so we get 

1/L = R(4)(1/4-1/16)
after solving this you will get ------
L = 4R/3 

now desired transition for H with same wavelength as that of he+
will be 

1/L  =  R(1²)(1/n1²-1/n2²)
put the value of L 


3R/4 =  R ( 1/n1²-1/n2²)
so by hit and trial method this will satisfy when 
 n1 = 1 and n2 = 2 .