Atomic Structure[ Quantum Physics ] A beam of electromagnetic radiation can be considered to be a stream of particles called photons.A photon is a quantum of electromagnetic radiation.Energy of a photon is given byE=hfPhotoelectric effect and line spectra provide evidence for the particulate nature of electromagnetic radiation.Phenomena such as interference and diffraction provide evidence for the wave nature of electromagnetic radiation.Photoelectric EffectThe photoelectric effect is the emission of electrons from a metal surface when electromagnetic radiation of sufficiently high frequency is shone on it.An experimental set-up to investigate photoelectric effect looks like this:

Monochromatic radiation strikes the cathode C and photoelectrons are emitted towards the anode A. When a potential difference V is applied, a current I is measured on the very sensitive ammeter. Data can also be obtained with the polarity of the supply reversed. Using this apparatus, the following graphs were obtained.

Einstein’s photoelectric equation states:hf = KEmax + ΦIn equation form,Energy of an incident photon is the sum of the maximum kinetic energy of the emitted electrons from the metal surface and the work function of the metal.Work function Φ = hfo where fo is the threshold frequency.KEmax = work done by stopping potential = eVs

Thus hf = eVs + hfo

The threshold frequency is the minimum frequency of the electromagnetic radiation below which no electrons are emitted from the metal surface regardless of the intensity of the radiation.The work function of a metal is the minimum energy needed to remove an electron from the metal surface.Line Spectra

An atom is in the ground state when its electron occupies the lowest energy level. When the atom gains energy, its electron makes a transition to a higher energy level. The atom is said to be in an excited state.The electron can jump to a lower energy level by emitting a photon whose energy is equal to the energy difference between the two levels. The photon energy is given byhf = Ehigher – Elower

The energy level diagram of hydrogen showing the transitions that lead to the emission line spectra looks like this:

Since the energy levels are discrete, photons of certain frequencies are emitted and thus line spectra are observed.

Emission line spectraIt is the spectrum of light radiated by individual atoms in a hot gas when the electrons in the atoms jump from higher energy levels to lower energy levels. The spectrum consists of coloured lines on a dark background.Absorption line spectraWhen a beam of white light is passed through a cool gas, photons whose energies are equal to the excitation energies of

the gas atoms, are absorbed. These photons are re-emitted in all directions, so the intensity of these wavelengths in the transmitted white light beam is reduced. An absorption spectrum consists of dark lines on a coloured background.Wave-particle dualityLouis de Broglie postulated that, because photons have wave and particle characteristics, perhaps all forms of matter have both properties. Electron diffraction provides evidence for the wave nature of particles.The de Broglie wavelength of a particle is given byλ = h/pwhere p is the momentum(mv) of the particle and h is Planck’s constant.X-raysX-rays are produced when electrons accelerated by a high voltage strike the metal target inside the X-ray tube.The X-ray spectrum consists of a continuous spectrum with a cutoff wavelength, λ min, which depends only on the voltage across the tube, and a series of peaks superimposed on it.

Explanation of the characteristic X-ray spectraElectrons accelerated by the high voltage can reach sufficient energies that when they collide with the atoms of the target, they can knock out one of the inner shell electrons. When an electron in an upper state drops down to fill the vacated lower state, a photon is emitted. This gives rise to the discrete lines in the X-ray spectra.Explanation of the continuous spectrumWhen electrons are decelerated by interaction with atoms of the target, photons are emitted whose energies are equal to the loss of kinetic energies of the electrons.The shortest wavelength X-ray produced is due to an electron losing all its kinetic energy to produce the highest energy photon in a single collision.Hence, hc/λmin = EK = eV where V is the accelerating voltage.The Heisenberg Uncertainty PrincipleHeisenberg’s position-momentum uncertainty principle is given by Δx Δp ≥ h/4πwhere Δx is the uncertainty in finding the position and Δp is the uncertainty in measuring the momentum of a particleHeisenberg’s time-energy uncertainty principle is given by ΔE Δt≥ h/4πThe Wave Function of a ParticleAn electron can be described by a wave function ψ where the square of the amplitude of the wave function lψl2 gives the probability of finding the electron at a point.Quantum TunnellingClassically, an electron of energy E approaching a potential barrier, whose height U is greater than E, cannot penetrate the barrier but would simply be reflected and return in the opposite direction.However, quantum mechanics predicts that since lψl2 is non-zero beyond the barrier, there is a finite chance of this electron tunnelling through the barrier and reaching the other side of the barrier.The transmission coefficient T represents the probability with which an approaching electron will penetrate to the other side of the barrier. The transmission coefficient T is given by

where m is the mass of the electron,d is the thickness of the barrier,U is the energy of the potential barrier,E is the energy carried by the electron.