# Light and Planck's Constant

1. Oct 19, 2005

### Soaring Crane

Ozone absorbs light having wavelengths of 2200 to 2900 angstroms protecting us from UV radiation. What are the frequencies and energy of the most energetic of these photons?

This is my workings:

E = h*v
lambda*v = c

2200 A *(10^-10 m / 1 A) = 2.2E-7 m
2900 A *(10^-10 m / 1 A) = 2.9E-7 m

v = (3.0 * 10^8 m/s)/lambda

v = (3.0 * 10^8 m/s)/2.2E-7 m = 1.4E15 s^-1
v = (3.0 * 10^8 m/s)/2.9E-7 m = 1.0E15 s^-1

E = (6.626*10^-34 J*s)*1.4E15 s^-1 = 9.0E-19 J Most energetic?
E = (6.626*10^-34 J*s)*1.0E15 s^-1 = 6.9E-19 J

Is this what is being asked?

Thanks.

2. Oct 19, 2005

### Staff: Mentor

Energy of a photon is proportional to its frequency $\nu$, with Planck's constant being the proportionality constant, i.e. Ephoton= h $\nu$, and the frequency is inversely proportional to wavelength, $\nu$ =c/$\lambda$,

so E = h c/$\lambda$,

So the energy of a photon is inversely proportional to wavelength, i.e. the shorter the wavelength, the greater the energy (or higher the frequency).