Question #1249f
1 Answer
Here;s how you can do that.
Explanation:
The idea here is that you must prove that the energy of a photon and its wavelength have an inverse relationship, i.e. when the wavelength increases, the energy decreases and vice versa.
To do that, you can start from the Planck - Einstein relation, which shows that the energy of a photon is directly proportional to its frequency
#color(blue)(ul(color(black)(E = h * nu)))#
Here
#E# is the energy of the photon#h# is Planck's constant, equal to#6.626 * 10^(-34)"J s"# #nu# is the frequency of the photon
Now, you should also know that frequency and wavelength have an inverse relationship as given by the equation
#color(blue)(ul(color(black)(nu * lamda = c)))#
Here
#lamda# is the wavelength of the wave#c# is the speed of light in a vacuum, usually given as#3 * 10^8"m s"^(-1)#
Rearrange this equation to find an expression for the frequency of the wave in terms of its wavelength
#nu * lamda = c implies nu = c/(lamda)#
Plug this into the Planck - Einstein relation to find
#E = h * c/(lamda)#
#color(darkgreen)(ul(color(black)(E = h * c * 1/(lamda))))#
Since the product between
#E = "constant" xx 1/(lamda)#
which is equivalent to
#E prop 1/(lamda)# The energy of a photon,
#E# , is inversely proportional to its wavelength,#lamda# , which is equivalent to saying that the energy of a photon is directly proportional to the inverse of its wavelength,#1/(lamda)#
You can even find a numeral value for the product between
#h * c = 6.626 * 10^(-34)"J" color(red)(cancel(color(black)("s"))) * 3 * 10^(8)"m" color(red)(cancel(color(black)("s"^(-1))))#
#h * c = 1.9878 * 10^(-25)"J m"#
This means that you have
#color(darkgreen)(ul(color(black)(E = 1.9878 * 10^(-25)"J m" * 1/(lamda))))#