What is the energy in joules of one photon of microwave radiation with a wavelength 0.122 m? (c = 2.9979 x 108 m/s; h = 6.626 x 10–34 J×s)

1 Answer
zhirou
Jun 14, 2018

#1.63xx10^-24 J#.

Explanation:

To answer this question, we'll need to use two equations:

  • #E = hν#,
  • and #c = λν#,

where #E# is energy in Joules, #h# is Planck's constant of #6.626xx10^-34# Joule-seconds, #ν# is frequency, #c# is the speed of light, which is #2.9979 xx 10^8 m//s#, and #λ# is wavelength in meters.

Since #ν# is in both equations, we can combine them:

#c = λν#

#ν = c/λ#

#E = hν#

#therefore E = (hc)/λ#

The question gives us a wavelength of #"0.122 m"#, so we can just plug that value into our equation and solve for #E#:

#E = (hc)/λ#

#E = ((6.626 xx 10^-34 J*s) xx (2.9979 xx 10^8 m//s))/"0.122 m"#

#= 1.63xx10^-24 J#

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