Question #83917
1 Answer
Explanation:
The idea here is that the energy of the photon is directly proportional to its frequency, as shown by the Planck - Einstein equation
#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
This equation basically tells you that the energy of a photon increases as its frequency increases.
Now, the problem wants you to find the wavelength of the photon; as you know, 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)#
Use the Planck - Einstein equation to find the frequency of the photon
#E = h * nu implies nu = E/h#
Plug in your value to find
#nu = (4.57 * 10^(-19)color(red)(cancel(color(black)("J"))))/(6.626 * 10^(-34)color(red)(cancel(color(black)("J")))"s"^(-1)) = 6.897 * 10^(14)#
Now use this value to find the wavelength of the photon
#nu * lamda = c implies lamda = c/(nu)#
Plug in your value to find
#lamda = (3 * 10^8 color(white)(.)"m" color(red)(cancel(color(black)("s"^(-1)))))/(6.897 * 10^(14)color(red)(cancel(color(black)("s"^(-1))))) = color(darkgreen)(ul(color(black)(4.35 * 10^(-7)"m")))#
The answer is rounded to three sig figs.