6.3: Atomic Line Spectra and Niels Bohr

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Rydberg Equation

Exercise \(\PageIndex{1}\)

What is the wavelength of light emitted when an electron in a hydrogen atom undergoes a transition from energy level n = 3 to level n = 1? (c = 3.00 × 10⁸ m/s, h = 6.63 × 10^–34 J·s, R_H = 2.179 × 10^–18 J)

Answer

102 nm

\[\frac{hc}{\lambda } = R_{H}\left [(\frac{1}{(n_{1})^{2}})-(\frac{1}{(n_{2})^{2}}) \right ]\]

\[\frac{(6.63*10^{-34})(3.00*10^{8})}{\lambda }=(2.179*10^{-18})(\frac{1}{1}-\frac{1}{9})\]
\[\lambda = \frac{1.981*10^{-25}}{1.937*10^{-18}}\]

\[\lambda = 1.023*10^{-7}\;m\]

Exercise \(\PageIndex{2}\)

The electron in a hydrogen atom, originally in level n = 5, undergoes a transition to a lower level by emitting a photon of wavelength 1583 nm. What is the final level of the electron? (c = 3.00 × 10⁸ m/s, h = 6.626 × 10^–34 J·s, R_H = 2.179 × 10^–18 J)

Answer: 3

Emission Lines

Exercise \(\PageIndex{3}\)

If a hydrogen atom in the excited n = 5 state relaxes to the ground state, what is the maximum number of possible emission lines?

Answer: 15

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