6.2: Quantization: Planck, Einstein, Energy, and Photons
- Page ID
- 168602
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Exercise \(\PageIndex{1}\)
What is the energy of a photon of electromagnetic radiation with a wavelength of 256.8 nm?
- Answer
-
7.714 x 10-19 J
\[E=\frac{h*c}{\lambda }\]
\[E=\frac{(6.625*10^{-34}\;J*s)*(2.99*10^{8}\;m/s)}{(256.8*10^{-9}\;m)}=7.7136*10^{-19}\;J\]
Exercise \(\PageIndex{2}\)
What is the wavelength of a photon that has an energy of 3.861 x 104 J
- Answer
-
5.130 x 10-21 nm
Exercise \(\PageIndex{3}\)
What is the energy of a photon of electromagnetic radiation with a frequency of 9.48 x 1014 Hz?
- Answer
-
6.28 x 10-19 J
Per Photon or Per Mole
Exercise \(\PageIndex{4}\)
A red laser pointer emits light at a wavelength of 580.9 nm. If the laser emits 1.84 × 10–4 J of energy per second in the form of visible radiation, how many photons per second are emitted from the laser?
- Answer
-
5.40 × 1014 photons/sec
\[E=\frac{hc}{\lambda }\]
\[E=\frac{(6.625*10^{-34}\;J/s)(2.99*10^{8}\;m/s)}{(580.9*10^{-9})\;m}=5.395*10^{14}\;photons/sec\]
Exercise \(\PageIndex{5}\)
What is the energy per mole of photons of light with a wavelength of 690.8 nm?
- Answer
-
8.210 × 102 kJ/mol
\[E_{per\;mole}=\frac{N_{a}hc}{\lambda }\]
\[E_{per\;mole}=\frac{(6.022*10^{23})(6.625*10^{-34})(2.99*0^{8})}{145.3*10^{-9}}=820979\;J/mol\]
Exercise \(\PageIndex{6}\)
What is the energy per mole of photons of light with a frequency of 2.98 × 1015 Hz?
- Answer
-
1.19 × 103 kJ/mol
Exercise \(\PageIndex{7}\)
If the energy of 1.00 mole of photons is 658 kJ, what is the wavelength of the light?
- Answer
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181 nm
Exercise \(\PageIndex{8}\)
A light emitting diode (L.E.D.) emits photons with an energy of 6.359 x 10-19 J. What is the energy per mole of photons emitted?
- Answer
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3.829 x 105 J/mol
Exercise \(\PageIndex{9}\)
What is the binding energy of an electron in a photosensitive metal (in kJ/mol) if the longest wavelength of light that can eject electrons from the metal is 459.0 nm?
- Answer
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259.9 kJ/mol
Exercise \(\PageIndex{10}\)
The energy required to break one mole of fluorine-fluorine bonds in F2 is 155 kJ/mol. What is the longest wavelength of light capable of breaking a single F-F bond?
- Answer
-
770 nm