Photons: Light Waves behaving as Particles

Photons:  Electromagnetic radiation behaves as both waves and particles.  The energy in an electromagnetic wave is carried in units called photons.  The energy E of one photon is proportional to the wave frequency f and inversely proportional to the wavelength \lambda, and is proportional to a universal quantity h called Planck’s constant: E=hf=\frac{hc}{\lambda}.  The momentum of a photon has magnitude E/c: p=\frac Ec=\frac{hf}c=\frac h{\lambda}.

The photo-electric effect:  In the photo-electric effect, a surface can eject an electron by absorbing a photon whose energy hf is greater than or equal to the work function \phi of the material.  The stopping potential V_0 is the voltage required to stop a current of ejected electrons from reaching an anode: eV_0=hf-\phi.

Photon production, photon scattering, and pair production:  X rays can be produced when electrons accelerated to high kinetic energy across a potential increase V_{AC} strike a target.  The photon model explains why the maximum frequency and minimum wavelength produced are given by the equation: eV_{AC}=hf_{\max}=\frac{hc}{\lambda_{\min}} (bremsstrahlung).  In Compton scattering a photon transfers some of its energy and momentum to an electron with which it collides.  For free electrons (mass m), the wavelengths of incident and scattered photons are related to the photon scattering angle \phi: \lambda'-\lambda=\frac{h}{mc}(1-\cos\phi) (Compton scattering).  In pair production a photon of sufficient energy can disappear and be replaced by electron-positron pair.  In the inverse process, an electron and positron can annihilate and be replaced by a pair of photons.

The Heisenberg uncertainty principle:  It is impossible to determine both a photon’s position and its momentum at the same time to arbitrarily high precision.  The precision of such measurements for the x-components is limited by the Heisenberg uncertainty principle, \Delta x\Delta p_x\geq\hbar/2; there are corresponding relationships for the y– and z-components.  The uncertainty \Delta E in the energy of a state that is occupied for a time \Delta t is given by equation \Delta t\Delta E\geq\hbar/2.  In these expressions, \hbar=h/2\pi.

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