6.2: Quantization: Planck, Einstein, Energy, and Photons

Chem 1402:General Chemistry I · LibreTexts

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    From LibreTexts, under CC BY-NC-SA 4.0, as the source states it; its equations are written in TeX, which the PDF shows typeset. This page at LibreTexts.

    Radiation and Planck's Constant

    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

    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

    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

    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

     

    6.2: Quantization: Planck, Einstein, Energy, and Photons is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by LibreTexts.