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 $x \times 1 0^{15} Hz$ . The value of x is ________
(Given $h = 4.25 \times 1 0^{- 15} e V s$ )

Question

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 $x \times 1 0^{15} Hz$ . The value of x is ________

(Given $h = 4.25 \times 1 0^{- 15} e V s$ )

TestHub · Accepted Answer

Let the higher state be n . The number of wavelengths emitted is given by, 2 n ( n − 1 ) ​ = 6 ⇒ n 2 − n − 12 = 0 ⇒ ( n − 4 ) ( n + 3 ) = 0 ⇒ n = 4 For hydrogen atom, h ν = 13.6 ( 1 1 ​ − 16 1 ​ ) = ( 13.6 × 16 15 ​ ) e V ⇒ ν = h E ​ = 16 × 6.62 × 1 0 − 34 13.6 × 15 × 1.6 × 1 0 − 19 ​ = 3 × 1 0 15 Hz

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