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Bohr's Model of a Hydrogen Atom

Wavelength of...

Question

Wavelength of a particular transition for H atom is 400 nm. What can be the wavelength of $H e^{+}$ for the same transition?

400 nm

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100 nm

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486 nm

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434 nm

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Solution

The correct option is B
100 nm
Wave number for hydrogen like species is give by

$\frac{1}{λ} = Z^{2} R_{H} (\frac{1}{n_{1}^{2}} - \frac{1}{n_{2}^{2}})$

$\frac{1}{400} = R_{H} (\frac{1}{n_{1}^{2}} - \frac{1}{n_{2}^{2}})$ for H atom
$\frac{1}{λ_{H e^{+}}} = 2^{2} R_{H} (\frac{1}{n_{1}^{2}} - \frac{1}{n_{2}^{2}})$

From the above equations,
$λ_{H e^{+}}$ = 100 nm

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Q. Wavelength of a particular transition for H atom is 400 nm. What can be the wavelength of

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Bohr's Model of a Hydrogen Atom

Standard XII Chemistry

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Wavelength of a particular transition for H atom is 400 nm. What can be the wavelength of He+ for the same transition?

The correct option is B 100 nmWave number for hydrogen like species is give by 1λ=Z2RH(1n21−1n22) 1400=RH(1n21−1n22) for H atom 1λHe+=22RH(1n21−1n22) From the above equations, λHe+ = 100 nm

Wavelength of a particular transition for H atom is 400 nm. What can be the wavelength of $H e^{+}$ for the same transition?