IIT JEE Advanced 2007 Paper 1

The largest wavelength (λ1) in the ultraviolet region is the first line of the Lyman series when the electron makes a transition from n = 2 to n = 1.

1

122

= RZ2(1−

1

4

) =

3

4

RZ2 (1)
The smallest wavelength in the infrared region is the last line of the Paschen series, when the electron makes a transition from n → ∞ to n = 3.

1

λ2

= RZ2(

1

9

−

1

∞

) =

1

9

RZ2 (2)
Dividing Eq. (1) by Eq. (2), we get

λ2

122

=

3

4

×9 =

27

4

⇒ λ2 =

122×27

4

= 823 nm