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Q.

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 $x \times 10^{15} Hz$ . The value of x is …… (Given $h = 4.25 \times 10^{- 15} eVs$ )

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Detailed Solution

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$\frac{(n - 1) n}{2} = 6 \Rightarrow n = 4$
The electron goes to $n = 4$
$∴ E = 13.6 (\frac{1}{1^{2}} - \frac{1}{4^{2}})$
$= 13.6 (\frac{15}{16}) ev$

$∴ E_{in} = hν = 13.6 (\frac{15}{16}) ev$

$\Rightarrow ν = \frac{13.6 (\frac{15}{16}) eV}{4.25 \times 10^{- 15} eVs} = \frac{13.6 \times 15}{16 \times 4.25} \times 10^{15} Hz$

$\Rightarrow ν = 3 \times 10^{15} Hz$

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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×1015 Hz . The value of x is …… (Given h=4.25×10−15eVs)