In which of the following transition, the wavelength will be minimum `:`

Options

A. `n_(4)rarr n_(1)`
B. `n_(2)rarr n_(1)`
C. `n_(4)rarr n_(2)`
D. `n_(3)rarr n_(1)`

Answer

A

Explanation

Minimum wavelength `rArr` Maximum frequency `rArr` Maximum enegry difference
`DeltaE = Z^(2)E_(1) ((1)/(n_(f)^(2))-(1)/(n_(i)^(2)))`
`DeltaE_(1) = Z^(2)E_(1) ((1)/(1^(2))-(1)/(4^(2))) = Z^(2)E_(1)((15)/(16))`
`DeltaE_(2) = Z^(2)E_(1) ((1)/(2^(2))-(1)/(1^(2))) = Z^(2)E_(1) ((3)/(4))`
`DeltaE_(3) = Z^(2)E_(1) ((1)/(2^(2))-(1)/(4^(2))) = Z^(2)E_(1) ((3)/(16))`
`DeltaE_(4) = Z^(2)E_(1) ((1)/(1^(2))-(1)/(3^(2))) = Z^(2)E_(1) ((8)/(9))`
Thus, `DeltaE_(1)` is the maximum.