Question #ab3dc
1 Answer
Explanation:
Start by calculating the energy of a single photon of wavelength
#"563 nm" = 563 color(red)(cancel(color(black)("nm"))) * "1 m"/(10^9color(red)(cancel(color(black)("nm")))) = 5.63 * 10^(-7)color(white)(.)"m"#
To do that, you can use the Planck - Einstein relation, which tells you that the energy of a photon,
#E = h * c/(lamda)#
Here
#h# is Planck's constant, equal to#6.626 * 10^(-34)color(white)(.)"J"# #c# is the speed of light in a vacuum, usually given as#3 * 10^8color(white)(.)"m s"^(-1)#
Plug in the value you have for the wavelength of the photon to get its energy--notice that I converted the wavelength to meters first!
#E = 6.626 * 10^(-34)color(white)(.)"J" color(red)(cancel(color(black)("s"))) * (3 * 10^8 color(red)(cancel(color(black)("m"))) color(red)(cancel(color(black)("s"^(-1)))))/(5.63 * 10^(-7)color(red)(cancel(color(black)("m"))))#
#E = 3.531 * 10^(-19)color(white)(.)"J"#
Now that you know the energy of a single photon of wavelength
#0.243 color(red)(cancel(color(black)("J"))) * "1 photon"/(3.531 * 10^(-19)color(red)(cancel(color(black)("J")))) = color(darkgreen)(ul(color(black)(6.88 * 10^(17)color(white)(.)"photons")))#
The answer is rounded to three sig figs.