What is the energy of a photon (J) that has a wavelength of 105 nm?

3.46

⋅

10

−

19

J

The energy of a photon is proportional to its frequency, as stated by the Planck - Einstein's equation

E

=

h

⋅

ν

, where

E

- the energy of the photon

h

- Planck's constant, equal to

6.626

⋅

10

−

34

J s

ν

- the frequency of the photon

Now, notice that you are given the wavelength of the photon,

λ

. As you know, frequency and wavelength have an inverse relationship described by the equation

λ

⋅

ν

=

c

, where

c

- the speed of light in vacuum, approximately equal to

3

⋅

10

8

m s

−

1

This means that the relationship between energy and wavelength looks like this

λ

⋅

ν

=

c

⇒

ν

=

c

λ

E

=

h

⋅

c

λ

Another important thing to notice here is that the wavelength of the photon is given in nanometers,

nm

. You need to convert this to meters, the unit used for the value of the speed of light.

E

=

6.626

⋅

10

−

34

J

s

⋅

3

⋅

10

8

m

s

−

575

⋅

10

−

9

m

=

3.46

⋅

10

−

19

J

Explanation:

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