18.Quantum Physics

A photon is a particle with zero rest mass consisting of a quantum of electromagnetic energy E, and E is equal to hf, where h is the Planck constant and f is the frequency of the electromagnetic radiation.

Wave-particle duality refers to the concept that all physical entities can be described either as waves or particles; the description to choose is entirely a matter of convenience. The two aspects; wave and particle, are linked through the two relations:

E = hf ; p = h/λ

On the left of each of these relations, E and p refer to a particle description. On the right, f and λ refer to a wave description.

The photoelectric effect is a phenomenon whereby electrons are emitted from the surface of the metal when a electromagnetic radiation of high enough frequency falls on the surface of a metal.

The threshold frequency is a certain minimum frequency of radiation below which no emission of electrons from the surface of the metal occurs irrespective of radiation intensity.

The work function energy of a metal is the minimum amount of energy that has to be given to an electron to release it from the surface of the metal.

The photoelectric phenomenon can be explained in terms of the photon energy E and work function energy φ. The maximum kinetic energy Kmax of the electrons emitted from the surface of the metal is given by

Kmax = E – φ

where Kmax = ½ m v2 max and E = hf.

Graph of current I against potential V

de Broglie’s equation suggests that a particle of mass m moving with speed v behaves in some ways like waves of wavelength λ given by

Emission line spectra consist of quite separate bright lines of definite wavelengths on a dark background and are given by luminous gases and vapours at low pressure in a discharge tube.

An absorption line spectrum is a continuous spectrum crossed by dark lines due to some missing frequencies and is produced when white light passes through a cooler gas or vapour.

The absorption spectrum is the inverse of the emission spectrum for the same element.

X-rays are electromagnetic waves whose wavelengths are in the range of 10 to 0.01 nanometre.

They possess the usual properties of such waves. They are shorter in wavelength than UV rays .

Bremsstrahlung describes the radiation which is emitted when fast-moving electrons are rapidly slowed down as they pass through the electric field around an atomic nucleus.

The Characteristic X-ray Spectrum is produced at high voltage as a result of specific electronic transitions that take place within individual atoms of the target material. The nucleus of the atom containing the protons and neutrons is surrounded by shells of electrons. The innermost shell, called the K-shell, is surrounded by the Land M-shells. When the energy of the bombarding electrons accelerated toward the target becomes high enough to dislodge K-shell electrons, electrons from the L- and M-shells move in to take the place of those dislodged and in the process produce x-rays with wavelengths that depend on the exact structure of the atom being bombarded.

The wave function Ψ is a variable quantity that mathematically describes the wave characteristics of a particle. It is related to the likelihood of the particle being at a given point in space at a given time, and may be thought of as an expression for the amplitude of the particle wave, though this is strictly not physically meaningful.

The square of the wave function [Ψ]2 is the significant quantity, as it gives the real physical probability for finding the particle at a given point in space and time.

Heisenberg showed that no matter how accurate the instruments used, quantum mechanics limits the precision when two properties are measured at the same time.

For the moving electron, if the properties are momentum and position, then Heisenberg showed that there is a limit to the accuracy you can measure these properties:

Δp Δx ≥h/2π

where Δx is the uncertainty in the measured position, Δp is the uncertainty in the momentum,

or if the properties are energy and time, then:

ΔE Δt ≥h/2π

Where Δt is the time interval during which the electron is in a state of energy E.

The term "potential barrier" is used when systems are described in terms of energy flow. Potential barrier acquires a more visual meaning when the energy flow is illustrated graphically in an energy diagram.

. In quantum mechanics, the rectangular potential barrier is a standard one-dimensional problem that demonstrates the phenomenon of quantum tunneling and wave-mechanical reflection.

Quantum Tunnelling is a quantum mechanical effect in which a particle has a finite probability of crossing a potential barrier even though the particle's energy is less than the potential barrier. Quantum tunnelling has no counterpart in classical mechanics, in which a particle can never cross a potential barrier with a higher energy level than the particle has.

The transmission coefficient T represents the probability current density of the transmitted wave relative to that of the incident wave. It is often used to describe the probability of a particle tunnelling through a barrier.

The reflection coefficient R represents the probability current density of the reflected wave relative to that of the incident wave.

Note that it can be shown that T + R = 1.

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