How to calculate the energy, in joules, of a photon of wavelength 5.00*10^4 nm ?

2 Answers
Mar 17, 2015

The energy of the photon is 3.97 × 10⁻²¹ J.

You have two useful formulas.

#E = hf#, where #h# is Planck's constant, and #f# is the frequency of the photon.

The other formula is

#fλ = c#, where #λ# is the wavelength of the photon and #c# is the speed of light.

Since #f = c/λ#, we can write

#E = (hc)/λ = (6.626 × 10⁻³⁴ "J·"cancel("s") × 2.998 × 10⁸cancel("m·s⁻¹"))/(5.00 × 10⁴ × 10⁻⁹cancel("m")) = 3.97 × 10⁻²¹"J"#

Mar 17, 2015

You calculate it like this:

#E=hf#

#E# = energy

#h# = Planck's Constant = #6.63xx10^(-34)"J.s"#

#c=flambda#

#c# speed of light =#3xx10^(8)"m/s"#

#f# frequency

#lambda# = wavelength = #5xx10^(4)"nm"=5xx10^(-5)"m"#

So first calculate the frequency of the photon:

#f=c/lambda = (3xx10^8)/(5xx10^(-5))=6xx10^(12)s^(-1)#

Then find the energy#rArr#

#E=hf#

#E=6.63xx10^(-34)xx6xx10^(12)"J"#

#E=3.98xx10^(-21)"J"#