Question

A light wave with a frequency of \( 6 \times 10^{14} \, \text{Hz} \) strikes a surface, and the incident power is \( 4 \times 10^{-3} \, \text{W} \). Calculate the energy of each photon.

• A. \( 5 \times 10^{15} \, \text{J/photon} \)
• B. \( 3 \times 10^{15} \, \text{J/photon} \)
• C. \( 5 \times 10^{10} \, \text{J/photon} \)
• D. \( 1 \times 10^{16} \, \text{J/photon} \)

Hint:

To calculate the energy of a photon, use the formula \( E = h \nu \), where \( \nu \) is the frequency of the light and \( h \) is Planck’s constant.

Answer 1

The Correct Option is A

Step 1: Using the energy formula for a photon.
The energy of a single photon can be calculated using Planck’s equation: \[ E = h \nu \] where \( E \) is the energy of the photon, \( h \) is Planck's constant (\( 6.63 \times 10^{-34} \, \text{J} \cdot \text{s} \)), and \( \nu \) is the frequency of the light.
Step 2: Substituting the values.
Given that the frequency \( \nu = 6 \times 10^{14} \, \text{Hz} \), we can substitute the values into the formula: \[ E = 6.63 \times 10^{-34} \times 6 \times 10^{14} = 5 \times 10^{-19} \, \text{J/photon} \]
Step 3: Conclusion.
The energy of each photon is \( 5 \times 10^{-19} \, \text{J/photon} \), which corresponds to option (A).