A monochromatic green light source used in a diffraction experiment has a wavelength of #5.80 *10^-7# m. What is the frequency of the light? What is the energy of a photon of this light?
1 Answer
Here's what I got.
Explanation:
The inverse relationship that exists between wavelength and frequency is described by the equation
#color(blue)( lamda * nu = c)" "# , where
Notice that the wavelength of the green light if given in meters and that the units used for the speed of light are meters per second. This tells you that you don't have to do any unit conversion before plugging in your value into the above equation.
So, the frequency of this green light will be
#lamda * nu = c implies nu = c/(lamda)#
#nu = (3 * 10^8 color(red)(cancel(color(black)("m"))) "s"^(-1))/(5.80 * 10^(-7)color(red)(cancel(color(black)("m")))) = 5.17 * 10^(14)"s"^(-1)#
As you know,
#"1 Hz" = "1 s"^(-1)#
Expressed in Hertz, the frequency of the light will be
#nu = color(green)(5.17 * 10^(14)"Hz"#
Now, the energy of an electromagnetic wave is directly proportional to that wave's frequency. This relationship is described by the Planck - Einstein equation, which looks like this
#color(blue)(E = h * nu)" "# , where
Notice that Planck's constant uses Joules second, which means that you're going to have to go back to
Once again, plug in your value to get
#E = 6.626 * 10^(-34)"J" color(red)(cancel(color(black)("s"))) * 5.17 * 10^(14)color(red)(cancel(color(black)("s"^(-1))))#
#E = color(green)(3.43 * 10^(-19)"J")#