18. Quantum Physics

18. Quantum Physics

[accordions autoHeight='true']

[accordion title="1. Particle Nature of Light"]

  • photon is a quantum of electromagnetic radiation.
  • The energy of a photon is given by E=hf, where h is Planck's constant (6.63 \times 10-34 J s) and f is its frequency.

[/accordion]

[accordion title="1.1 Photoelectric Effect"]

  • The photoelectric effect is the emission of electrons from a metal surface when electromagnetic radiation of sufficiently high frequency is shone on it.
  • The energy of an incident photon is the sum of the maximum kinetic energy K.E._{max} of the emitted electrons from the metal surface and the work function \Phi of the metal. Einstein's photoelectric equation states that

hf=\Phi +K.E._{max}=hf_o +K.E._{max}

  • where f_o is the threshold frequency or 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 \Phi of a metal is the minimum energy needed to remove an electron from the metal surface.
  • K.E._{max} can be measured by applying a voltage to prevent the emitted electrons from reaching the electrode that collects them. This voltage is known as the stopping voltage V_s and since the charge of an electron is e, the equation can be rewritten as

hf=\Phi + eV_s.

[/accordion]

[accordion title="1.2 Line Spectra"]

  • An atom is in the ground state when its electron occupies the lowest energy level. When the atom gains energy, its ground state electron makes a transition to a higher energy level. The atom is said to be in an excited state.
  • At this excited state, the electron is unstable. It will 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 hf = Ehigher – Elower.
  • The emission line spectra are the spectra 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. Each spectrum consists of coloured lines on a dark background.
  • The absorption line spectra consists of dark lines on a coloured background. When 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.

[/accordion]

[accordion title="2. Wave Nature of Particles"]

  • Louis 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 by \lambda = \dfrac{h}{p} where p is the momentum (mv) of the particle and h is Planck’s constant.

[/accordion]

[accordion title="3. X-ray Spectrum"]

[/accordion]

[accordion title="4. Heisenberg Uncertainty Principle"]

[/accordion]

[accordion title="5. Wave Function and Probability"]

  • An electron can be described by a wave function \Psi where the square of the amplitude of the wave function |{\Psi}|^2 gives the probability of finding the electron at a point.

[/accordion]

[accordion title="6. Quantum Tunneling"]

  • Classically, 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 |{\Psi}^2| 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 T=e^{-2kd} where k=\sqrt{\dfrac{8\pi^2m(U-E)}{h^2}}

[/accordion]

[/accordions]