# 18. Quantum Physics

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[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  10-34 J s) and f is its frequency.

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[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  of the emitted electrons from the metal surface and the work function  of the metal. Einstein's photoelectric equation states that



• where  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  of a metal is the minimum energy needed to remove an electron from the metal surface.
•  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  and since the charge of an electron is e, the equation can be rewritten as

.

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[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.

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[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  where p is the momentum (mv) of the particle and h is Planck’s constant.

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

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

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

• An electron can be described by a wave function  where the square of the amplitude of the wave function  gives the probability of finding the electron at a point.

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[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  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 

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