What is the energy of a photon of blue light with a wavelength of 460 nm?

We want to find the energy of a photon given that we know its wavelength.

We will see that the energy of the photon is:

Now let's see how to get the

The energy of a photon of wavelength λ is given by:

Where:

So we need to rewrite our wavelength in meters instead of nanometers, so the units coincide.

we know that:

Then:

Now that we know all the values we need to use in the energy equation, we can write:

So we just found the energy of the photon.

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Explanation:

The energy of a photon is given by:

(1)

Where:

is the Planck constant

is the frequency light

On the other hand, there is an inverse relationship between  and the wavelength :

(2)

Where:

is the speed of light

is the wavelength

Substituting (2) in (1):

(3)

Finally:

This is the energy of a photon of blue light, in Joules.

causes

fossil fuels burn

cities become more industrialized

human population grows worldwide