Momentum Of A Photon

Although a photon has zero rest mass, it still carries linear momentum given by $p=\frac{h}{\lambda }=\frac{E}{c}$, a relation that follows from combining $E=h\nu$ with the relativistic energy-momentum result $E=pc$ for massless particles. This momentum is responsible for radiation pressure exerted by light on a surface. Substituting $h=6.6\times 10^{-34}\text{J s}$ and $\lambda =5\times 10^{-7}\text{m}$ gives $p=\frac{6.6\times 10^{-34}}{5\times 10^{-7}}=1.32\times 10^{-27}{\text{kg m s}}^{-1}$. The value $2.64\times 10^{-27}$ wrongly halves the wavelength. The value $6.60\times 10^{-28}$ doubles the wavelength. The value $3.30\times 10^{-27}$ uses an incorrect wavelength near $2\times 10^{-7}\text{m}$. The same de Broglie relation $p=h/\lambda$ links photons and matter waves, a unifying idea stressed in the dual-nature chapter. A check on magnitude shows the momentum is extremely small, which is why the mechanical push of ordinary light is imperceptible yet measurable in sensitive experiments. Importantly, although the photon is massless, its momentum is real and measurable, and the cumulative momentum of countless photons produces a steady force called radiation pressure. This pressure, though tiny for ordinary light, drives the tails of comets away from the Sun and is the operating principle behind proposed solar-sail spacecraft, illustrating that light genuinely carries mechanical momentum.