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
1. What is the fine-structure constant (α) in simple terms?
The fine-structure constant, represented by the Greek letter alpha (α), is a fundamental physical constant that quantifies the strength of the electromagnetic interaction between elementary charged particles. It is a dimensionless quantity, meaning it has no units, and its value is approximately 1/137. It essentially defines how strongly particles like electrons and photons interact with each other.
2. What is the formula for the fine-structure constant?
The fine-structure constant (α) is defined by a combination of three other fundamental constants of nature. The formula is:
α = e² / (4πε₀ħc)
Where:
- e is the elementary charge (the charge of a single proton or electron).
- ε₀ is the vacuum permittivity (a constant of electromagnetism).
- ħ is the reduced Planck constant (a key constant in quantum mechanics).
- c is the speed of light in a vacuum (a key constant in relativity).
3. What is the currently accepted numerical value of the fine-structure constant?
The currently accepted value of the fine-structure constant (α) is approximately 0.0072973525693(11). For easier understanding and general calculations in physics, it is often approximated by the fraction 1/137. However, it's important to remember that it is not exactly 1/137.
4. Why is the fine-structure constant dimensionless (i.e., has no units)?
The fine-structure constant is dimensionless because it is a ratio of energies or speeds. In its most common definition, it is the square of the ratio of the elementary charge to the Planck charge. Alternatively, it can be seen as the ratio of the speed of an electron in the first circular orbit of the Bohr model of the atom to the speed of light in a vacuum. Since it is a ratio of two quantities with the same units (charge/charge or speed/speed), the units cancel out, leaving a pure number.
5. How does the fine-structure constant relate to the splitting of spectral lines in atoms?
The fine-structure constant gets its name from its role in explaining the 'fine structure' in atomic spectra. Simple models of the atom predict single spectral lines for electron transitions. However, high-resolution spectroscopy reveals these lines are actually composed of several closely spaced, finer lines. This splitting is caused by relativistic effects and spin-orbit coupling. The magnitude of this splitting is directly proportional to α², making the fine-structure constant essential for accurately predicting the energy levels of atoms as per the CBSE Class 12 syllabus on atomic structure.
6. Why is the value of the fine-structure constant, approximately 1/137, considered so significant in physics?
The significance of α ≈ 1/137 is a subject of great fascination. Physicist Richard Feynman called it 'one of the greatest damn mysteries of physics'. Its importance stems from several points:
- It's a pure number: It doesn't depend on the system of units used. An alien civilization would measure the exact same value.
- It sets the scale: Its small value is why we can use perturbation theory in quantum electrodynamics (QED) to make incredibly precise calculations. If it were much larger, atoms might not be stable.
- Unification of Theories: Its formula uniquely combines constants from electromagnetism (e), relativity (c), and quantum mechanics (ħ), hinting at a deep connection between these theories.
7. Is the fine-structure constant a true universal constant, or can its value change?
While it is considered a fundamental constant, one of the open questions in modern physics is whether its value has been the same throughout the history of the universe. Some astronomical observations of distant quasars have suggested that α might have been slightly different billions of years ago. However, these results are not yet conclusive, and other experiments have found no evidence of change. The current scientific consensus, as applied in standard models, treats it as a constant, but research into its potential variation is ongoing.
8. How does the fine-structure constant determine if an atom can hold on to its electrons?
The fine-structure constant is crucial for atomic stability. For elements with a very high atomic number (Z), the innermost electrons orbit at relativistic speeds. Theory predicts that if the value of Z becomes greater than approximately 1/α (which is about 137), the ground state energy of the innermost electron would become imaginary. This implies that the electromagnetic force would be so strong that a stable nucleus with Z > 137 could not exist with a complete electron shell, as it would spontaneously create electron-positron pairs from the vacuum. This makes α a key factor in defining the upper limits of the periodic table.
