Question

a single photon has an energy of 3.550 ×10^-19. Calculate the enrgy of one mole of photons assuming you have light at a wavelength of 640nm

Answer 1

To calculate the energy of one mole of photons, we can follow these steps:

1. We know the energy of a single photon \( E \) is given as \( 3.550 \times 10^{-19} \) Joules.

2. To find the energy of one mole of photons, we multiply the energy of a single photon by Avogadro's number, which is approximately \( 6.022 \times 10^{23} \) mol\(^{-1}\).

\[
E_{\text{mole}} = E \times N_A
\]

Where:
- \(E_{\text{mole}}\) is the energy of one mole of photons.
- \(E\) is the energy of a single photon.
- \(N_A\) is Avogadro's number.

3. Plugging in the values:

\[
E_{\text{mole}} = (3.550 \times 10^{-19} \, \text{J}) \times (6.022 \times 10^{23} \, \text{mol}^{-1})
\]

4. Now calculating:

\[
E_{\text{mole}} = 3.550 \times 6.022 \times 10^{4} \, \text{J}
\]

Calculating that:

\[
E_{\text{mole}} \approx 2.1391 \times 10^5 \, \text{J}
\]

5. Therefore, the energy of one mole of photons at a wavelength of 640 nm is approximately:

\[
E_{\text{mole}} \approx 2.14 \times 10^5 \, \text{J}
\]

This means that one mole of photons at this wavelength has an energy of about 214 kJ.