What is the formula for calculating energy using wavelength?

The formula for calculating energy using wavelength is derived from the relationship between energy, wavelength, and the constants that describe electromagnetic radiation. In option A, the formula ( E = \frac{h \cdot c}{\text{wavelength}} ) successfully captures this relationship, where ( E ) represents energy, ( h ) is Planck's constant (( 6.626 \times 10^{-34} , \text{J s} )), and ( c ) is the speed of light in a vacuum (( 3.00 \times 10^8 , \text{m/s} )).

This equation arises from the understanding that energy can also be expressed in a wave context. More specifically, the energy of a photon is inversely proportional to its wavelength—shorter wavelengths correspond to higher energy photons, and vice versa. This is fundamental in fields such as quantum mechanics and photonics.

Other options represent different physical relationships. For instance, ( E = mc^2 ) is Einstein's mass-energy equivalence formula, applicable in nuclear physics rather than for photon energy. The formula ( E = kT ) relates energy to temperature in statistical mechanics, specifically for particles in a