Among the following transition in hydrogen and hydrogen-like spectrum, which one emits light of lngest wavelength ?

Options

A. `n = 2` "to" `n = 1` "for" `H`
B. `n = 4` "to"` n = 3` "for"` Li^(2+)`
C. `n = 4` "to" `n = 3` "for" `He^(o+)`
D. `n = 5` "to" `n = 2` "for" `H`

Answer

C

Explanation

Longest `lambda` or shortest E
a. `(1)/(lambda) = R ((1)/(1) - (1)/(4)) = (3R)/(4) = 0.75 R`
b.`(1)/(lambda) = R xx Z^(2)((1)/(3^(2)) - (1)/(4^(2))) = R xx 9 xx (7)/(114) = 0.4375 R`
c.`(1)/(lambda) = R xx 2^(2)((1)/(3^(2)) - (1)/(4^(2))) = R xx 4 xx (7)/(114) = 0.194R`
`(1)/(lambda) = R ((1)/(2^(2)) - (1)/(5^(2))) = R xx (21)/(100) = 0.21 R`
Lowest value of `1//lambda` highest value of `lambda` is in c