What is the wavelength of a photon of energy of #5.518 * 10^-26# joules?

1 Answer
Jun 10, 2016

The length of the wave corresponding to the energy mentioned is about #3.59m#

Explanation:

The link between the energy of a photon and its wavelength can be shown in a formula:

#E=h*f#, where #E# is energy, #h# is Planck's constant and #f# is the frequency.

This formula uses wave's frequency, but it can be rearranged so that it uses the length using the formula:

#f=c/lambda#

If we combine both formulas we get:

#E=(hc)/lambda#, so if we calculate the wavelength we get:

#lambda=(hc)/E#

Now we just have to substitute the values:

#lambda=(6.62xx10^-34xx3xx10^8)/(5.518xx10^-26)#

#lambda=(6.62xx3xx10^-26)/(5.518xx10^-26)#

Now we can reduce the expressions with exponents and calculate just multiplication and division:

#lambda=(6.62xx3)/5.518~~3.59#

Finally we have to calculate the units:

#[m]=[(J*s*m)/(J*s)]=[m]#

This calculation shows that the formula is correct.