Green light has a wavelength of 5200 A. How do you calculate the energy of one photon of green light?

1 Answer
Aug 15, 2017

Answer:

#E = 3.8xx10^-19# #"J"#

Explanation:

We're asked to calculate the energy of one photon of a green light, given its wavelength of #5200# #"Å"#.

To do this, we can use the equation

#ul(E = (hc)/f#

where

  • #E# is the energy of the photon (in joules)

  • #h# is Planck's constant, equal to #6.626xx10^-34# #"J"•"s"#

  • #c# is the speed of light in vacuum, #299792458# #"m/s"#

  • #f# is the frequency of the photon (in meters)

We need to convert from ångströms to meters, using the conversion factor

#1# #"m"# #= 10^10# #"Å"#:

#5200cancel("Å")((1color(white)(l)"m")/(10^10cancel("Å"))) = color(red)(ul(5.2xx10^-7color(white)(l)"m"#

The energy of the photon is thus

#color(blue)(E) = ((6.626xx10^-34color(white)(l)"J"•cancel("s"))(299792458cancel("m/s")))/(color(red)(5.2xx10^-7cancel("m"))) = color(blue)(ulbar(|stackrel(" ")(" "3.8xx10^-19color(white)(l)"J"" ")|)#

rounded to #2# significant figures.