A monochromatic light is incident on a hydrogen sample in ground state. Hydrogen atoms absorb a fraction of light and subsequently emit radiation of six different wavelengths. The frequency of incident light is x × 10 15 Hz . The value of x is ________ (Given h = 4 . 25 × 10 - 15 eVs )

Step-by-step solution

Let the higher state be n . The number of wavelengths emitted is given by, n ( n - 1 ) 2 = 6 ⇒ n 2 - n - 12 = 0 ⇒ n - 4 ( n + 3 ) = 0 ⇒ n = 4 For hydrogen atom, h ν = 13 . 6 1 1 - 1 16 = 13 . 6 × 15 16 eV ⇒ ν = E h = 13 .6 × 15 × 1 . 6 × 10 - 19 16 × 6 . 62 × 10 - 34 = 3 × 10 15 Hz