Quantum mechanics part -2

   

                                                      Quantum mechanics part -2

The first quantum Theory: Max Planck and black-body radiation: Thermal Radiation is electromagnetic radiation emitted from the surface of an object due to the object's internal energy. If an object is heated sufficiently, it starts to emit light at the red end of the visible spectrum, as it becomes red hot.

Heating it further causes the color to change from red to yellow, white, and blue, as it emits light at increasingly shorter wavelengths (higher frequencies). A perfect emitter is also a perfect absorber: when it is cold, such an object looks perfectly black, because it absorbs all the light that falls on it and emits none. Consequently, an ideal thermal emitter is known as a black body, and the radiation it emits is called black body radiation.

The first model that was able to explain the full spectrum of thermal radiation was put forward by Max Planck in 1900. He proposed a mathematical model in which the thermal radiation was in equilibrium with a set of Harmonic oscillators.

reproduce the experimental results, he had to assume that each oscillator emitted an integer number of units of energy at its single characteristic frequency, rather than being able to emit any arbitrary amount of energy. In other words, the energy emitted by an oscillator was quantized. The quantum of energy for each oscillator, according to Planck, was proportional to the frequency of the oscillator; the constant of proportionality is now known as the Planck Constant. The Planck constant, usually written as h, has the value of 6.63×10⁻³⁴ J⋅s. So, the energy E of an oscillator of frequency f is given by 

To change the color of such a radiating body, it is necessary to change its temperature. Planck's Law explains why: increasing the temperature of a body allows it to emit more energy overall, and means that a larger proportion of the energy is towards the violet end of the spectrum.

Planck's law was the first quantum theory in physics, and Planck won the Nobel Prize in 1918 "in recognition of the services he rendered to the advancement of Physics by his discovery of energy quanta". At the time, however, Planck's view was that quantization was purely a heuristic mathematical construct, rather than (as is now believed) a fundamental change in our understanding of the world.

Max Karl Ernst  Ludwig  Planck

The Second Quantum Theory:   Photons: the Quantization of Light: In 1905, Albert Einstein took an extra step. He suggested that quantization was not just a mathematical construct, but that the energy in a beam of light actually occurs in individual packets, which are now called photons. The energy of a single photon of light of frequency  is given by the frequency multiplied by Planck's constant  (an extremely tiny positive number):

${\displaystyle �=ℎ�}$

For centuries, scientists had debated between two possible theories of light: was it a wave or did it instead comprise a stream of tiny particles? By the 19th century, the debate was generally considered to have been settled in favor of the wave theory, as it was able to explain observed effects such as refraction, diffraction, interference, and polarisation.

 James Clerk Maxwell had shown that electricity, magnetism, and light are all manifestations of the same phenomenon: the electromagnetic field. Maxwell's equation, which is the complete set of laws of classical electromagnetism, describes light as waves: a combination of oscillating electric and magnetic fields. Because of the preponderance of evidence in favor of the wave theory, Einstein's ideas were met initially with great skepticism. Eventually, however, the photon model became favored. 

One of the most significant pieces of evidence in its favor was its ability to explain several puzzling properties of the photoelectric effect, described in the following section. Nonetheless, the wave analogy remained indispensable for helping to understand other characteristics of light: diffraction, refraction, and interference.

 

The Third quantum Theory:   The Photoelectric effect:  In 1887, Heinrich Hertz observed that when light with sufficient frequency hits a metallic surface, the surface emits electrons.

 In 1902, Philipp Lenard discovered that the maximum possible energy of an ejected electron is related to the frequency of the light, not to its intensity: if the frequency is too low, no electrons are ejected regardless of the intensity. Strong beams of light toward the red end of the spectrum might produce no electrical potential at all, while weak beams of light toward the violet end of the spectrum would produce higher and higher voltages. The lowest frequency of light that can cause electrons to be emitted, called the threshold frequency, is different for different metals. 

This observation is at odds with classical electromagnetism, which predicts that the electron's energy should be proportional to the intensity of the incident radiation. So when physicists first discovered devices exhibiting the photoelectric effect, they initially expected that a higher intensity of light would produce a higher voltage from the photoelectric device.

Einstein explained the effect by postulating that a beam of light is a stream of particles ("photons") and that, if the beam is of frequency f, then each photon has an energy equal to hf.  

An electron is likely to be struck only by a single photon, which imparts at most an energy hf to the electron. Therefore, the intensity of the beam has no effect and only its frequency determines the maximum energy that can be imparted to the electron.

To explain the threshold effect, Einstein argued that it takes a certain amount of energy, called the work function and denoted by φ, to remove an electron from the metal. This amount of energy is different for each metal. If the energy of the photon is less than the work function, then it does not carry sufficient energy to remove the electron from the metal. The threshold frequency, f₀, is the frequency of a photon whose energy is equal to the work function:

${\displaystyle �=ℎ{�}_0.}$

If f is greater than f₀, the energy hf is enough to remove an electron. The ejected electron has a kinetic energy, E_K, which is, at most, equal to the photon's energy minus the energy needed to dislodge the electron from the metal:

${\displaystyle {�}_{�}=ℎ�-�=ℎ(�-{�}_0).}$

Einstein's description of light as being composed of particles extended Planck's notion of quantized energy, which is that a single photon of a given frequency, f, delivers an invariant amount of energy, hf. In other words, individual photons can deliver more or less energy, but only depending on their frequencies. In nature, single photons are rarely encountered. 

The Sun and emission sources available in the 19th century emitted vast numbers of photons every second, so the importance of the energy carried by each photon was not obvious. Einstein's idea that the energy contained in individual units of light depends on their frequency made it possible to explain experimental results that had seemed counterintuitive. 

However, although the photon is a particle, it was still described as having the wave-like property of frequency. Effectively, the account of light as a particle is insufficient, and its wave-like nature is still required.

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Other parts of Quantum Mechanics provide in the next blog.

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