Light and Planck's Constant

[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.

 

[Astronuc]

Energy of a photon is proportional to its frequency $\nu$, with Planck's constant being the proportionality constant, i.e. E_photon= 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).

 

[quicknote]

Yes, you have correctly calculated the frequencies and energy of the most energetic photons in the given range of wavelengths. The most energetic photon has a frequency of 1.4E15 s^-1 and an energy of 9.0E-19 J, while the next most energetic photon has a frequency of 1.0E15 s^-1 and an energy of 6.9E-19 J. These energetic photons are able to be absorbed by ozone molecules, providing protection from harmful UV radiation. Planck's constant, denoted by h, plays a crucial role in determining the energy of a photon, as shown in the equation E = h*v. This demonstrates the importance of understanding and utilizing fundamental scientific principles, such as Planck's constant, in our daily lives.