What equation is used to measure the energy of a photon? \( \mathrm{PE}=\mathrm{mgh} \) \( \mathrm{KE}=1 / 2 \mathrm{mv}^{2} \) \( \mathrm{E}=\Delta \mathrm{mc}^{2} \) \( \mathrm{E}=\mathrm{hf} \)

The equation that is used to measure the energy of a photon is \( \mathrm{E}=\mathrm{hf} \), where \( \mathrm{E} \) stands for energy, \( \mathrm{h} \) is Planck's constant, and \( \mathrm{f} \) is the frequency of the photon. This equation encapsulates the idea that photons, the packets of light energy, have energy that is directly proportional to their frequency—higher frequency means more energy, which is why ultraviolet light can cause sunburns while infrared light cannot. If you're curious about how this plays out in real life, consider solar panels! They convert sunlight (which is made of photons) into electrical energy using this principle. The frequency of the light that hits the panel determines how much energy can be captured and transformed into usable electricity. It's a brilliant application of quantum physics that energizes our homes!