Question

Green light has the wavelength of 5.0x 10^2 nm. what is the energy, in joules, of one photon of green light?

Answer 1

Answer:

$3.96\text{ }\times\text{ 10}^{-19}\text{ J}$

Explanation:

Here, we want to get the energy in Joules

Given:

$\begin{gathered} wavelength\text{ \lparen}\lambda)\text{ = 5.02 }\times\text{ 10}^2\text{ nm} \\ 1\text{ nm = 1}\times\text{ 10}^{-9}\text{ m} \\ wavelength\text{ = 5.02 }\times\text{ 10}^{-7}\text{ m} \end{gathered}$

The frequency of light can be calculated using the formula as follows:

$\begin{gathered} f\text{= }\frac{c}{\lambda} \\ \\ c\text{ = speed of light = 3 }\times\text{ 10}^8\text{ ms}^{-1} \end{gathered}$

Calculating the frequency, we have it that:

$\text{ f = }\frac{3\times10^8}{5.02\times10^{-7}}\text{ = 5.98 }\times\text{ 10}^{14}\text{ S}^{-1}$

The Energy of a photon is calculated as:

$\begin{gathered} E\text{ = hf} \\ h\text{ = Planck's constant = 6.626 }\times\text{ 10}^{-34}\text{ Js} \end{gathered}$

We proceed to multiply this with the frequency above as follows:

$E\text{ = 6.626 }\times\text{ 10}^{-34}\times\text{ 5.98 }\times\text{ 10}^{14}\text{ = 3.96 }\times\text{ 10}^{-19}\text{ J}$