Calculate the energy of one mole of photon of radiation of:a) Frequency 4.6 GHz

To calculate the energy of one mole of photons of radiation with a frequency of 4.6 GHz, we can use the equation:

E = h * f

where E is the energy of one photon, h is the Planck's constant (6.62607015 × 10^-34 J·s), and f is the frequency of the radiation.

First, we need to convert the frequency from GHz to Hz. Since 1 GHz is equal to 10^9 Hz, the frequency becomes:

f = 4.6 GHz * 10^9 Hz/GHz = 4.6 × 10^9 Hz

Now, we can substitute the values into the equation:

E = (6.62607015 × 10^-34 J·s) * (4.6 × 10^9 Hz)

Calculating this expression gives us the energy of one photon. However, we need to find the energy of one mole of photons.

To convert from energy per photon to energy per mole of photons, we need to multiply by Avogadro's number (6.02214076 × 10^23 mol^-1):

Energy per mole = E * Avogadro's number

Substituting the value of E into the equation:

Energy per mole = [(6.62607015 × 10^-34 J·s) * (4.6 × 10^9 Hz)] * (6.02214076 × 10^23 mol^-1)

Calculating this expression will give us the energy of one mole of photons of radiation with a frequency of 4.6 GHz.