Question

The line spectrum of lithium has a red line at 670.8 nm. Calculate the energy of a photon with this wavelength.

Answer 1

First of all, we can calculate the frequency of the photon, which is related to the wavelength by the following equation:
$f= \frac{c}{\lambda}$
where c is the speed of light and $\lambda=670.8 nm=670.8 \cdot 10^{-9} m$ is the photon wavelength. Substituting into the formula, we find the frequency
$f= \frac{c}{\lambda}= \frac{3 \cdot 10^8 m/s}{670.8 \cdot 10^{-9} m}=4.47 \cdot 10^{14} Hz$

Now we can find the energy of the photon with the following equation:
$E=hf$
where h is the Planck constant. Substituting numbers, we find
$E=hf=(6.6 \cdot 10^{-34}Js)(4.47 \cdot 10^{14} Hz)=2.95 \cdot 10^{-19} J$