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

Feb 11, 2016

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