Calculate the energy, in joules, of a photon of green light having a wavelength of 562nm?

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Meave60 Share
Sep 10, 2017

The answer is #3.54xx"10"^(-19)" J"#.

The equation for determining the energy of a photon of electromagnetic radiation is #E=hnu#, where E is energy in Joules, h is Planck's constant, #6.626 xx"10"^(-34)"J"*"s"#, and #nu# (pronounced "noo") is the frequency.

You have been given the wavelength #lambda# (pronounced lambda) in nanometers, but not the frequency.

Fortunately, a relationship between wavelength, frequency, and the speed of light, #c# exists, such that #c=lambda*nu#. To determine the frequency from the wavelength, divide #c# by #lambda#:

#nu=(c)/(lambda)#

We can substitute #(c)/(lambda)# for #nu# in the first equation, so that:

#E=h*(c)/(lambda)#

The speed of light, #c#, is usually given as #3.00xx10^8"m/s"# rounded to three significant figures. So the wavelength must first be converted from nm to m. #1 "m"=1xx10^9 "nm"#. To convert nm to m, do the following calculation:

#562 color(red)cancel(color(black)( "nm"))xx(1"m")/(1xx10^9 color(red)cancel(color(black)("nm")))="0.000000562m"=5.62xx"10"^(-7) "m"#

Now we're ready to determine the amount of energy in Joules in one photon of green light with the wavelength #"562 nm"#.

#E=hnu=h*(c)/(lambda)#

Substitute the known values into the equation and solve.

#6.626xx"10"^(-34)"J"*color(red)cancel(color(black)("s"))xx(3.00xx"10"^8color(red)cancel(color(black)("m"))/color(red)cancel(color(black)("s")))/(5.62xx"10"^(-7)color(red)cancel(color(black)("m")))=3.54xx"10"^(-19)" J"#

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Michael Share
Apr 6, 2015

#E=3.537xx10^(-19)"J"#

#E=hf=(hc)/(lambda)#

#E=(6.626xx10^(-34)xx3xx10^8)/(562xx10^(-9))"J"#

#E=3.537xx10^(-19)"J"#

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