Question

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

Answer 1

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"`

Answer 2

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"`