Solution by Substitution

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

E=h(nu)                                       (I) 

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


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:


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


(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 .