A beam of light having wavelength distributed uniformly between $450 n m$ to $550 n m$ passes through a sample of hydrogen gas. Which wavelength will have the least intensity in the transmitted beam?

$487 n m$

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$91.6 n m$

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$468 n m$

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$512 n m$

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Solution

The correct option is A
$487 n m$

$Δ E_{m a x} = \frac{h c}{450} = 2.76 e V$
$Δ E_{m i n} = \frac{h c}{λ} = 2.25 e V$

The absorption of energy by the $H_{2}$ atom which lies exactly between these two is $2.55 e V$ from $n = 2$ to $n = 4$ , hence wavelength which has been absorbed by hydrogen is $λ = \frac{h c}{2.25} = 487 n m$

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A beam of light having wavelength distributed uniformly between 450 nm to 550 nm passes through a sample of hydrogen gas. Which wavelength will have the least intensity in the transmitted beam?

The correct option is A 487 nm ΔEmax=hc450=2.76eV ΔEmin=hcλ=2.25eV The absorption of energy by the H2 atom which lies exactly between these two is 2.55 eV from n=2 to n=4, hence wavelength which has been absorbed by hydrogen is λ=hc2.25=487 nm

A beam of light having wavelength distributed uniformly between $450 n m$ to $550 n m$ passes through a sample of hydrogen gas. Which wavelength will have the least intensity in the transmitted beam?