Question

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

Answer 1

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.