Question

What total energy (in kJ) is contained in 1.0 mol of photons, all with a frequency of 2.75 × 10^14 Hz?

a) 457 kJ
b) 110 kJ
c) 219 kJ
d) 326 kJ

Answer 1

The total energy contained in 1.0 mol of photons with a frequency of 2.75 × 10^14 Hz is 110 kJ, calculated using the energy equation for photons and multiplying by Avogadro's number.

Step-by-step explanation:

To calculate the total energy contained in 1.0 mol of photons with a frequency of 2.75 × 10^14 Hz, we use the equation E = hν, where E is the energy of one photon, h is Planck's constant (6.626 × 10^-34 J·s), and ν is the frequency of the photon. We then multiply the energy of one photon by Avogadro's number (6.022 × 10^23 mol^-1) to find the energy contained in 1 mole of photons.

First, calculate the energy of one photon:

E = (6.626 × 10^-34 J·s) × (2.75 × 10^14 Hz) = 1.822 × 10^-19 J

Next, calculate the energy contained in 1 mole of photons:

E_total = (1.822 × 10^-19 J/photon) × (6.022 × 10^23 photons/mol)

E_total = 1.097 × 10^5 J/mol = 109.7 kJ/mol

Therefore, the correct answer is (b) 110 kJ.