Question

What is the energy of a blue light with a wavelength of 545 nm?

Answer 1

The energy of one photon of that light is 3.65 x `10^-19` joules.

Explanation:

To find energy, you must know the frequency of the light. Since we are given wavelength we can use this equation: c= `lambda`v where c is the speed of light (3 x `10^8` m/s), `lambda` is the wavelength, and the v is the frequency (units: 1/s). However, since the speed light is in m/s, you have to convert nanometers to meters.
(545nm)(m/ `10^9` nm) = 5.45 x `10^-7` m (nanometers cancel out)

Plug in c and wavelength
3 x `10^8` m/s= (5.45 x `10^-7` m)v
solve for v by dividing both sides by the wavelength
v= 5.50 x `10^14` 1/s
Now that we have frequency, you can use the equation: E= hv where E is energy per photon, h is planck's constant which is 6.626 x `10^-34` joule/second, and v is frequency.

E= (6.626 x `10^-34` joule/second)(5.50 x `10^14` 1/s)
seconds cancel out leaving you with
E = 3.65 x `10^-19` joules