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"#
