Question

If light has a wavelength of `692nm`, then calculate the energy of these photons in Joules?

Answer 1

`2.87 xx 10^-19 "J"`

Explanation:

The energy `E` of a photon can be calculated if the frequency is known, as related by the equation

`E = hf`

where `f` is the frequency in `"s"^-1`, and
`h` is called Planck's constant, equal to `6.626 xx 10^-34 "J"*"s"`.

We don't know the frequency of this photon yet, but we can find it using the equation `f = c/lambda`

where `gamma` is the wavelength of the photon (in `"m"`), and
`c` is the speed of light in a vacuum, equal to `299,792,458 "m"/"s"`.

We can combine these two equations to yield

`E = (hc)/lambda`.

Plugging in known variables, the energy of the photon (in `"J"`), is

`E = ((6.626 xx 10^-34 "J"*"s")(299,792,458 "m"/"s"))/(6.92 xx 10^-7 "m") = color(red)(2.87 xx 10^-19 "J"`