Photon Momentum

Although a photon has no rest mass, NCERT shows that it carries momentum given by $p=\frac{h}{\lambda }$, a relation that follows from combining $E=h\nu$ with the relativistic result $E=pc$ for a massless particle. Substituting $h=6.63\times 10^{-34}$ J·s and $\lambda =0.2\times 10^{-9}=2\times 10^{-10}$ m gives $p=\frac{6.63\times 10^{-34}}{2\times 10^{-10}}=3.3\times 10^{-24}$ kg·m/s. This momentum, though tiny, is what allows radiation to exert pressure on surfaces. The value $3.3\times 10^{-27}$ kg·m/s is wrong because it mishandles the nanometre-to-metre conversion by three orders of magnitude. The value $1.3\times 10^{-24}$ kg·m/s is wrong because it uses an incorrect wavelength of about 0.5 nm rather than 0.2 nm. The value $6.6\times 10^{-34}$ kg·m/s is wrong because it merely restates Planck's constant without dividing by the wavelength. As stated in NCERT Class 12, Chapter 11, photon momentum is inversely proportional to wavelength, so short-wavelength X-rays carry substantial momentum per photon. This momentum relation also explains radiation pressure: when photons strike and are absorbed or reflected by a surface, they transfer this momentum, exerting a measurable force per unit area. Because short-wavelength X-ray photons carry far more momentum than visible photons, they interact strongly with matter and are used in techniques such as Compton scattering. A magnitude check confirms that a 0.2 nm X-ray photon should carry appreciably more momentum than a visible photon, consistent with the small wavelength.