Wavelengths for organic chemistry

Question

The equipment used for aviation communications emits high‑frequency radiowave energy with a wavelength of 0.250 km. What is the energy of exactly one photon of this radiowave radiation?

E=

What is the energy of one mole of this radiowave radiation? E=

Answer 1

For this problem, you want to first make sure you convert from km to meters, keeping in mind that there are 1000 m in 1 km: 0.250 km (1000 m / 1 km) = 250. m

Then you can use the equation E = hc/λ (where E is the energy, h is Planck's constant, c is the speed of light, and λ is the wavelength in m): E = ((6.626 x 10^-34J*s) * (2.998 x 10⁸m/s)) / (250. m) = J/photon

After that, you will convert from J/photon (the energy you will calculate above will be in J/photon as we are calculating from wavelength, and the wavelength of each individual photon due to light being quantized) using Avogadro's number: J/photon (6.022 x 10²³ photon / 1 mol) = J/mol

You should get values on the order of 10^-28 J/photon and 10^-4 J/mol, respectively with 3 significant figures. Hope that helps.