A mole of red photon of wavelength 725nm has how much KJ?

Question

A mole of red photons with a wavelength of 725 nm has how much energy in kilojoules (kJ)? 
Here’s what I have done so far:

I converted the wavelength from nanometers to meters: 
   ( 725 \, 	ext{nm} = 725 	imes 10^{-9} \, 	ext{m} = 7.25 	imes 10^{-7} \, 	ext{m} ).

I calculated the energy using the formula ( E = \frac{hc}{	ext{wavelength}} ):
   [
   E = \frac{(6.626 	imes 10^{-34} \, 	ext{J s})(3.0 	imes 10^8 \, 	ext{m/s})}{7.25 	imes 10^{-7} \, 	ext{m}} = 2.74 	imes 10^{-19} \, 	ext{J}.
   ]

I noticed that the answer states it should be 165 kJ. However, even if I convert the energy I calculated to kJ, it doesn't match that value.

I also tried using the formula ( E = hv ) where ( v = \frac{c}{	ext{wavelength}} ):
   [
   v = \frac{3.0 	imes 10^8 \, 	ext{m/s}}{7.25 	imes 10^{-7} \, 	ext{m}} = 4.14 	imes 10^{14} \, 	ext{Hz},
   ]
   and then calculated:
   [
   E = (6.626 	imes 10^{-34} \, 	ext{J s})(4.14 	imes 10^{14} \, 	ext{Hz}) = 2.75 	imes 10^{-19} \, 	ext{J}.
   ]

I am unsure why my calculations do not yield the correct answer. Does it matter whether I use ( E = \frac{hc}{	ext{wavelength}} ) or ( E = hv ) (finding ( v ) through ( v = \frac{c}{	ext{wavelength}} )? Thank you for your assistance!

Anonymous · Accepted Answer

You have successfully completed the first step of the problem which was to compute the energy of a single photon. You simply need to multiply that energy by the number of photons in a mole of photons (6.02E23)
If I use your first calculated energy of a photon, 2.75E-19J*6.02E23=166kJ

Anonymous

A mole of red photon of wavelength 725nm has how much KJ?

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