6.3: Atomic Line Spectra and Niels Bohr
- Page ID
- 168603
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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, RH = 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, RH = 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