Light that has a frequency of about a wavelength of about 683 nm appears red to our eyes. What is the energy in joules of the photons associated with this light?
The energy of a photon can be calculated using the formula:
\[E = hf\]
where:
- \(E\) is the energy of the photon,
- \(h\) is Planck's constant (\(6.626 x 10^{-34}\) J s),
- \(f\) is the frequency of the light.
First, we need to convert the wavelength to frequency using the formula:
\[c = \lambda f\]
where:
- \(c\) is the speed of light (\(3.00 x 10^8\) m/s),
- \(\lambda\) is the wavelength.
Since the wavelength is 683 nm (\(683 x 10^{-9}\) m), we can now calculate the frequency:
\[f = \frac{c}{\lambda} = \frac{3.00 x 10^8}{683 x 10^{-9}} = 4.39 x 10^{14} Hz\]
Now, we can calculate the energy of the photon:
\[E = (6.626 x 10^{-34})(4.39 x 10^{14}) = 2.91 x 10^{-19} J\]
Therefore, the energy of a photon associated with light having a wavelength of about 683 nm is \(2.91 x 10^{-19}\) Joules.