# Green light has a wavelength of 5200 A. How do you calculate the energy of one photon of green light?

Aug 15, 2017

$E = 3.8 \times {10}^{-} 19$ $\text{J}$

#### Explanation:

We're asked to calculate the energy of one photon of a green light, given its wavelength of $5200$ $\text{Å}$.

To do this, we can use the equation

ul(E = (hc)/f

where

• $E$ is the energy of the photon (in joules)

• $h$ is Planck's constant, equal to $6.626 \times {10}^{-} 34$ $\text{J"•"s}$

• $c$ is the speed of light in vacuum, $299792458$ $\text{m/s}$

• $f$ is the frequency of the photon (in meters)

We need to convert from ångströms to meters, using the conversion factor

$1$ $\text{m}$ $= {10}^{10}$ $\text{Å}$:

5200cancel("Å")((1color(white)(l)"m")/(10^10cancel("Å"))) = color(red)(ul(5.2xx10^-7color(white)(l)"m"

The energy of the photon is thus

$\textcolor{b l u e}{E} = \left(\left(6.626 \times {10}^{-} 34 \textcolor{w h i t e}{l} \text{J"•cancel("s"))(299792458cancel("m/s")))/(color(red)(5.2xx10^-7cancel("m"))) = color(blue)(ulbar(|stackrel(" ")(" "3.8xx10^-19color(white)(l)"J"" }\right) |\right)$

rounded to $2$ significant figures.