If the longest wavelength of the ultraviolet region of hydrogen spectrum is `lambda_(0)` then the shortest wavelength of its infrared region is ......

Options

A. `(46)/(7)lambda_(0)`
B. `(20)/(3)lambda_(0)`
C. `(36)/(5)lambda_(0)`
D. `(27)/(4)lambda_(0)`

Answer

A

Explanation

For maximum wavelength of ultravioli spectrum n = 2,
`:.(1)/(lambda_(0))=R[(1)/(l^(2))-(1)/(n^(2))]`
`=R[1-(1)/(4)]`
`(1)/(lambda_(0))=(3R)/(4) .....(1)`
For minimum wavelength of infrared spectrum for Paschen series, n = 0
`(1)/(lambda)=R[(1)/(3^(2))-(1)/(n^(2))]`
`=R[(1)/(9)-(1)/(oo^(2))]`
`=(R)/(9)....(2)`
By taking ratio of (1) and (2)
`(lambda)/(lambda_(0))=(3R)/(4)xx(9)/(R)`
`:. lambda=(27)/(4)lambda_(0)`