In the following example, we are given one equation that relates the energy of a photon (E) to its frequency ( ) by means of a proportionality constant called Planck's constant (h). The equation is:

(I)

We are also told that the speed of light (c) is always equal to the product of the photon's frequency ( ) and wavelength ( ):

(II)

In a typical problem, we might be given the energy (E) of a particular
photon and asked to find its wavelength ( ).
The speed of light *c* is always known, so we must find a
relationship between what is unknown (the wavelength) and those
quantities that are known (energy and speed of light).

In Eq. **(I)**, we must replace
, which is unknown. To do this, solve Eq **(II) **to obtain
an expression for in terms
of and c:

(III)( (found by dividing both sides of(II)by )

In Eq. **(I)**, replace
with the above equivalence:

(IV)

Solve Eq **(IV) **to isolate the only unknown quantity (
) on the left side:

(V)

(found by multiplying both sides by and dividing both sides by E)

Now substitute in numerical values for h, c, and E into Eq. **(V)
**and you obtain a numerical result for the wavelength .