The blue color of the sky results from the scattering of sunlight by molecules in the air. The blue light has a frequency of about 7.5×1014Hz a) Calculate the wavelength (in nm) associated with this radiation, and b) calculate the energy (in joules) of a single photon associated with this frequency.

Question

The blue color of the sky results from the scattering of sunlight by molecules in the air. The blue light has a frequency of about 7.5×1014Hz  a) Calculate the wavelength (in nm) associated with this radiation, and  b) calculate the energy (in joules) of a single photon associated with this frequency.

Ethan Sanders · Accepted Answer

Step 1&amp;nbsp;Part A:&amp;nbsp;Use the speed of light equation to calculate the wavelength corresponding to this frequency.&amp;nbsp;x=λν&amp;nbsp;⇒λ=cν&amp;nbsp;=2.998×108ms7.5×1014s−1&amp;nbsp;=4.0×10−7m&amp;nbsp;Determine the wavelength of this photon in units of nanometers:&amp;nbsp;1. Begin with the wavelength in meters.&amp;nbsp;2. Use a conversion factor to convert meters into nanometers.&amp;nbsp;λ=4.0×10−7m1nm&amp;nbsp;10−9m=4.0×102nm&amp;nbsp;Step 2&amp;nbsp;Part B:&amp;nbsp;Use the equation for the energy of a photon to calculate the energy of this photon&amp;nbsp;E=hν&amp;nbsp;=(6.626×10−34J×s)(7.5×1014s−1)&amp;nbsp;=5.0×10−19J

Anzante2m · Accepted Answer

Step 1  Given:  The frequency of light =7.5×1014Hz  Calculating the wavelength:  Relation between frequency and wavelength: λ=νc  c=3×108ms  ν=7.5×1014Hz  Substitute the known values in the above formula and simplify,  λ=7.5×1014Hz3×108ms  =0.4×10−6m  =400×10−9m  And, 1nm=10−9m  =400nm  λ=400nm  Step 2  The energy of a single photon associated with the frequency:  Formula: E=hν   h=placonstant=6.63×10−34  ν=7.5×1014Hz  E=6.63×10−34×7.5×1014Hz  =49.695×10−20J  =4.9695×10−19J  E=4.9695×10−19J

Accepted Answer

B)4.97×10^-19 J

The blue color of the sky results from the scattering

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