We know that the fine structure constant is identical to the constant of Sommerfeld in modern physics. It is symbolized by the Greek letter α (alpha) and is a physical constant having no dimension.
This constant portrays the strong point of electromagnetic force exchanges between any two fundamental charged particles.
The physical clarification of Fine Structure Constant is numerous. Some illustrations about the fine structure constant are listed below-
α is a one-fourth product of the characteristic impedance of free space in electrical engineering and solid-state physics.
Fine Structure Constant α is directly proportional to the coupling constant in quantum electrodynamics.
α provides the possibility of emission or absorption of an electron by a photon.
α offers the extreme positive charge of an atomic nucleus under the Bohr model that will let a stable-orbit around it.
It possesses a wide range of uses in low energy physics, mainly in electro-weak theory. Similarly, some properties of subatomic particles show a definite correlation with α.
Fine Constant
Fine-Structure Constant has the identical numerical value in all system of units only because it is a dimensionless quantity, which is about
\[\alpha = \frac{1}{137} = 0.0072973535664 (17)\]
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Structure Constant
Alpha (α) known as the fine structure constant, defines the electromagnetic radiation which influences charged particles.
The numerical value of the alpha (α) is 0.007297352, having a misgiving of 6 in the last decimal place so that it is one of the finest dignified numbers in physics.
Fine Number Constant
The Fine-Structure Constant describes the effectiveness or capacity of the coupling of any elementary charged particle (e) with the specified electromagnetic field.
By representing it in the mathematical aspect, α can be represented like other fundamental physical constants as given below-
\[\alpha = \frac{1}{4 \pi \epsilon_{0}} \frac{e^{2}}{(\frac{\hbar}{2 \pi})c} = \frac{\mu_{0}}{4 \pi} \frac{e^{2}c}{(\frac{\hbar}{2 \pi})c} = \frac{k_{\epsilon}e^{2}}{(\frac{\hbar}{2 \pi}) c} = \frac{c \mu_{0}}{2 R_{K}} = \frac{e^{2}}{4 \pi} \frac{Z_{0}}{(\frac{\hbar}{2 T})}\]
Here,
e is the elementary charge (e = 1.602176634 × 10-19 C)
\[\hbar = \frac{h}{2 \pi}\] where ħ is the reduced Plank’s constant.
ε0 = permittivity of free space.
c = velocity of light in vacuum (c = 299792458 m/s)
Ke = Coulomb constant.
RK = von Klitzing constant.
Z0 = impedance of free space.
µ0 = Permeability of free space.
Fine Structure Constant Explained
‘α’ known as the fine structure constant, is a quantity of the strong point of the electromagnetic coupling constant at minimum energies. The fine structure constant is one of the utmost significance of our system of fundamental constants.
The rest energy of the electron gives the size of the various transition energies in atoms. This elementary constant also calculates the Josephson Effect and the quantum Hall effect in condensed matter physics.
We accept the measurement of the electron magnetic moment in 2008 as given below
\[\alpha = \frac{1}{4 \pi \epsilon_{0}} \frac{e^{2}}{\hbar}{c}\]
Fine Structure Constant Derivation
The best and precise calculation of the fine structure constant (α) derives from our 2008 measurement of the electron magnetic moment along with QED calculations.
As per the result, the experimental uncertainty is obtained as 0.24 ppb while the experimental error is obtained as 0.28 ppb, for a mutual uncertainty of 0.37 ppb.
This calculation about the fine structure constant is 12 and 20 times more precise than that of the next most accurate independent calculations (Rb 2008 and Cs 2006). A part per billion is specified by ppb = 10-9.
\[\alpha^{-1} = 137.035999084 (33} (39) [0.24 ppb][0.28 ppb] = 137.035999084 (51)[0.37 ppb]\]
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QED also known as Quantum electrodynamics theory shares the electron magnetic moment in Bohr magnetons (titled g/2) to the fine structure constant α. QED calculations in a very extraordinary way define the Ck.
The minor alterations considered as ax with numerous subscripts are minor modifications that are supposed to be well-understood under the standard model of particle physics.
In a modern evaluation, we formulate the best values for these constants and the computations from which they originated.
\[\frac{g}{2} = 1 + C_{2} (\frac{\alpha}{\pi}) + C_{4} (\frac{\alpha}{\pi})^{2} + C_{6} (\frac{\alpha}{\pi})^{3} + C_{8}(\frac{\alpha}{\pi})^{4} + C_{10} (\frac{\alpha}{\pi})^{5} + . . . + \alpha_{\mu \tau} + \alpha_{hadronic} + \alpha_{weak}\]
As we can determine g/2 in a better and precise way than the fine structure constant, α can be determined by any liberated means, the maximum precise magnitude of α comes from reversing this expression to measure this constant regarding the measured g/2.
Therefore, our calculation of the fine structure constant assumes that the standard model of particle physics is correct.
The absolute calculations of the fine structure constant in conjunction with our more precise measurement, originate from measurements of the Rydberg constant, an optical frequency, and atom recoil using atom interferometry.
From recent reviews, we obtained the most perfect measurements of the fine structure constant.
Fine structure constant alpha
The magnitude of the dimensionless physical quantity can be stated in numerous units.
Natural Unit
Natural units are generally used in High energy physics, where ε0 = c = ћ = 1. At this point, ε0 is the permittivity of free space. Therefore, the measurement of fine structure constant originates as given below:
\[\alpha = \frac{e^{i}}{4 \pi}\]
Atomic Units
As per the atomic units, \[\epsilon_{0} = \frac{1}{d \pi}\] and e = \[m_{e} = \hbar = 1\], so the fine structure constant can be illustrated as:
\[\alpha = \frac{1}{c}\]
Electrostatic CGS Unit
In these CGS units, electric charge is determined by using statcoulomb and it is explained by assuming permittivity factor 4πε0 or Coulomb constant Ke is 1 and it is dimensionless.
This is why the magnitude of fine structure constant turns out to be:
\[\alpha = \frac{e^{e}}{(\frac{h}{2 \pi})c\]
FAQs on Fine Structure Constant
Q1. Do you have any Idea Regarding the Origin of the Fine Structure Constant?
Ans: We express the fine structure constant (α) as the ratio between the energy required surpassing the electrostatic repulsion urging these electrons apart and single-photon energy whose wavelength is 2π multiplied by the distance within the electrons.
Q2. Why is ‘137’ an Enchanted Sum?
Ans: As per Lederman The number 137 appears uncovered all over the place. It means that if scientists are using for the calculation of all the types of units for the charge on any planet in the universe, will all come up with 137 since it is a pure number.
They use charge or speed, and whatever their version of Planck's constant may be, the value will be 137.
Q3. Who has Exposed the Fine Structure Constant?
Ans: Arnold Sommerfeld presented the fine structure constant into physics as a description of the splitting of atomic spectral lines.
After some years, the fine structure constant (α) was revealed as a legitimately universal constant, appearing universally in the physics of Atomic-Scale systems and quantum electrodynamics.
Q4. Does the Fine Structure Constant Vary?
Ans: No!
The fine structure constant does not alter in time. At that time, they observed how their effects are suitable with more recent answers: that the fine structure constant differs with direction.
Former outcomes have revealed that the fine structure is somewhat different from a specific axis of the Universe, named a dipole.
