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

Md Ariful Islam

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Md Ariful Islam

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

To do this, we can use the equation

$ul(E = (hc)/f$

where

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

  • $h$ is , equal to $6.626xx10^-34$ $"J"•"s"$

  • $c$ is the speed of light in vacuum, $299792458$ $"m/s"$

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

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

$1$ $"m"$ $= 10^10$ $"Å"$:

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

The energy of the photon is thus

$color(blue)(E) = ((6.626xx10^-34color(white)(l)"J"•cancel("s"))(299792458cancel("m/s")))/(color(red)(5.2xx10^-7cancel("m"))) = color(blue)(ulbar(|stackrel(" ")(" "3.8xx10^-19color(white)(l)"J"" ")|)$

rounded to $2$ .

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