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

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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