A beam of ultraviolet radiation having wavelength between $100 n m$ and $200 n m$ is incident on a sample of atomic hydrogen gas. Assuming that the atoms are in ground state, which wavelengths will have low intensity in the transmitted beam?

104 n m

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103 n m

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105 n m

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100 n m

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Solution

The correct option is A $103 n m$
Energy corresponding to wavelength 100nm, $\frac{1242 e V}{100} = 12.42 e V$
Energy corresponding to wavelength 200nm, $\frac{1242 e V}{200} = 6.21 e V$
Energy required from ground state to first excited stage:
$E_{2} - E_{1} = 13.6 - 3.4 = 10.2 e V$
Energy required from ground state to second excited stage:
$E_{3} - E_{1} = 13.6 - 13.6 - 1.5 = 12.1 e V$
Energy required from ground state to third excited stage:
$E_{3} - E_{1} = 13.6 - 0.85 = 12.75 e V$
At 10.2 eV,
$W a v e l e n g t h 1 = \frac{1242}{10.2} = 122 n m$
At 12.1 eV,
$W a v e l e n g t h 2 = \frac{1242}{12.1} = 103 n m$

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A beam of ultraviolet radiation having wavelength between 100nm and 200nm is incident on a sample of atomic hydrogen gas. Assuming that the atoms are in ground state, which wavelengths will have low intensity in the transmitted beam?

A beam of ultraviolet radiation having wavelength between $100 n m$ and $200 n m$ is incident on a sample of atomic hydrogen gas. Assuming that the atoms are in ground state, which wavelengths will have low intensity in the transmitted beam?