Questions: A photon has a frequency of 3.80 × 10^7 Hz. Calculate the energy (in joules) of 1 mole of photons with this frequency. Be sure your answer has the correct number of significant digits.

Solution Steps

The energy of a single photon can be calculated using the formula: \[ E = h \cdot f \] where \( E \) is the energy of the photon, \( h \) is Planck's constant (\(6.6261 \times 10^{-34} \, \text{J} \cdot \text{s}\)), and \( f \) is the frequency of the photon.

Given: \[ f = 3.80 \times 10^{7} \, \text{Hz} \]

Substitute the values into the formula: \[ E = (6.6261 \times 10^{-34} \, \text{J} \cdot \text{s}) \cdot (3.80 \times 10^{7} \, \text{Hz}) \]

Calculate \( E \): \[ E = 2.5180 \times 10^{-26} \, \text{J} \]

To find the energy of 1 mole of photons, multiply the energy of a single photon by Avogadro's number (\(6.0221 \times 10^{23} \, \text{mol}^{-1}\)).

\[ E_{\text{mole}} = E \cdot N_A \] \[ E_{\text{mole}} = (2.5180 \times 10^{-26} \, \text{J}) \cdot (6.0221 \times 10^{23} \, \text{mol}^{-1}) \]

Calculate \( E_{\text{mole}} \): \[ E_{\text{mole}} = 1.516 \times 10^{1} \, \text{J/mol} \]

Final Answer