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According to special relativity, the kinetic energy (i.e., the difference between the total energy and the rest mass energy) of a particle of rest mass \(m\) and momentum \(p\) is \[T = \sqrt{p^{\,2}\,c^{\,2}+m^{\,2}\,c^{\,4}} - m\,c^{\,2}.\] In the non-relativistic limit \(p\ll m\,c\), we can expand the square-root in the previous expression to give \[T = \frac{p^{\,2}}{2\,m}\left[1- \frac{1}{4}\left(\frac{p}{m\,c}\right)^2+ {\cal O}\left(\frac{p}{m\,c}\right)^4\right].\] Hence, \[T \simeq \frac{p^{\,2}}{2\,m} - \frac{p^{\,4}}{8\,m^{\,3}\,c^{\,2}}.\] Of course, we recognize the first term on the right-hand side of this equation as the standard non-relativistic expression for the kinetic energy. The second term is the lowest-order relativistic correction to this energy. Let us consider the effect of this type of correction on the energy levels of a hydrogen atom. So, the unperturbed Hamiltonian is given by Equation ([e12.58]), and the perturbing Hamiltonian takes the form \[H_1 = - \frac{p^{\,4}}{8\,m_e^{\,3}\,c^{\,2}}.\]

Now, according to standard first-order perturbation theory (see Section 1.4), the lowest-order relativistic correction to the energy of a hydrogen atom state characterized by the standard quantum numbers \(n\), \(l\), and \(m\) is given by \[\begin{aligned} {\mit\Delta} E_{nlm} &= \langle n,l,m|H_1|n,l,m\rangle = - \frac{1}{8\,m_e^{\,3}\,c^{\,2}}\, \langle n,l,m|p^{\,4}|n,l,m\rangle\nonumber\\[0.5ex] &= - \frac{1}{8\,m_e^{\,3}\,c^{\,2}}\, \langle n,l,m|p^{\,2}\,p^{\,2}|n,l,m\rangle.\end{aligned}\] However, Schrödinger’s equation for a unperturbed hydrogen atom can be written \[p^{\,2}\,\psi_{n,l,m} = 2\,m_e\,(E_n-V)\,\psi_{n,l,m},\] where \(V=-e^{\,2}/(4\pi\,\epsilon_0\,r)\). Because \(p^{\,2}\) is an Hermitian operator, it follows that \[\begin{aligned} {\mit\Delta} E_{nlm} &= -\frac{1}{2\,m_e\,c^{\,2}}\,\langle n,l,m|(E_n -V)^{\,2}|n,l,m\rangle\nonumber\\[0.5ex] &= -\frac{1}{2\,m_e\,c^{\,2}}\left(E_n^{\,2} - 2\,E_n\,\langle n,l,m|V|n,l,m\rangle + \langle n,l,m|V^{\,2}|n,l,m\rangle\right)\nonumber\\[0.5ex] &= -\frac{1}{2\,m_e\,c^{\,2}}\left[ E_n^{\,2} + 2\,E_n\left(\frac{e^{\,2}}{4\pi\,\epsilon_0}\right)\left\langle \frac{1}{r}\right\rangle + \left(\frac{e^{\,2}}{4\pi\,\epsilon_0}\right)^2\left\langle\frac{1}{r^{\,2}}\right\rangle\right].\end{aligned}\] It follows from Equations ([e9.74]) and ([e9.75]) that \[\begin{aligned} {\mit\Delta} E_{nlm} &= -\frac{1}{2\,m_e\,c^{\,2}}\left[ E_n^{\,2} + 2\,E_n\left(\frac{e^{\,2}}{4\pi\,\epsilon_0}\right)\frac{1}{n^{\,2}\,a_0} + \left(\frac{e^{\,2}}{4\pi\,\epsilon_0}\right)^2\frac{1}{(l+1/2)\,n^{\,3}\,a_0^{\,2}}\right].\nonumber\\[0.5ex]&\end{aligned}\] Finally, making use of Equations ([e9.55]), ([e9.56]), and ([e9.57]), the previous expression reduces to

\[\label{e12.121} {\mit\Delta} E_{nlm} = E_n\,\frac{\alpha^{\,2}}{n^{\,2}}\left(\frac{n}{l+1/2}-\frac{3}{4}\right),\] where \[\alpha = \frac{e^{\,2}}{4\pi\,\epsilon_0\,\hbar\,c}\simeq \frac{1}{137}\] is the dimensionless *fine structure constant*.

Note that the previous derivation implicitly assumes that \(p^{\,4}\) is an Hermitian operator. It turns out that this is not the case for \(l=0\) states. However, somewhat fortuitously, our calculation still gives the correct answer when \(l=0\) . Note, also, that we are able to employ non-degenerate perturbation theory in the previous calculation, using the \(\psi_{nlm}\) eigenstates, because the perturbing Hamiltonian commutes with both \(L^2\) and \(L_z\). It follows that there is no coupling between states with different \(l\) and \(m\) quantum numbers. Hence, all coupled states have different \(n\) quantum numbers, and therefore have different energies.

Now, an electron in a hydrogen atom experiences an electric field \[{\bf E} = \frac{e\,{\bf r}}{4\pi\epsilon_0\,r^{\,3}}\] due to the charge on the nucleus. However, according to electromagnetic theory, a non-relativistic particle moving in a electric field \({\bf E}\) with velocity \({\bf v}\) also experiences an effective magnetic field

\begin{equation}\mathbf{B}=-\frac{\mathbf{v} \times \mathbf{E}}{c^{2}}\end{equation} Recall, that an electron possesses a magnetic moment [see Equations ([e10.58]) and ([e10.59])] \[\mu = - \frac{e}{m_e}\,{\bf S}\] due to its spin angular momentum, \({\bf S}\). We, therefore, expect an additional contribution to the Hamiltonian of a hydrogen atom of the form [see Equation ([e10.60a])] \[\begin{aligned} H_1 = - \mu\cdot {\bf B}=- \frac{e^{\,2}}{4\pi\,\epsilon_0\,m_e\,c^{\,2}\,r^{\,3}}\,{\bf v}\times {\bf r}\cdot{\bf S}= \frac{e^{\,2}}{4\pi\,\epsilon_0\,m_e^{\,2}\,c^{\,2}\,r^{\,3}}\,{\bf L}\cdot {\bf S},\end{aligned}\] where \({\bf L} = m_e\,{\bf r}\times {\bf v}\) is the electron’s orbital angular momentum. This effect is known as *spin-orbit coupling*. It turns out that the previous expression is too large, by a factor 2, due to an obscure relativistic effect known as *Thomas precession* . Hence, the true spin-orbit correction to the Hamiltonian is

\[\label{e12.127} H_1 = \frac{e^{\,2}}{8\pi\,\epsilon_0\,m_e^{\,2}\,c^{\,2}\,r^{\,3}}\,{\bf L}\cdot {\bf S}.\] Let us now apply perturbation theory to the hydrogen atom, using the previous expression as the perturbing Hamiltonian.

Now, \[{\bf J} = {\bf L} + {\bf S}\] is the total angular momentum of the system. Hence, \[J^{\,2} = L^2+S^2+ 2\,{\bf L}\cdot{\bf S},\] giving \[{\bf L}\cdot {\bf S} = \frac{1}{2}\,(J^{\,2}-L^2-S^2).\] Recall, from Section [s11.2], that while \(J^{\,2}\) commutes with both \(L^2\) and \(S^2\), it does not commute with either \(L_z\) or \(S_z\). It follows that the perturbing Hamiltonian ([e12.127]) also commutes with both \(L^2\) and \(S^2\), but does not commute with either \(L_z\) or \(S_z\). Hence, the simultaneous eigenstates of the unperturbed Hamiltonian ([e12.58]) and the perturbing Hamiltonian ([e12.127]) are the same as the simultaneous eigenstates of \(L^2\), \(S^2\), and \(J^{\,2}\) discussed in Section [s11.3]. It is important to know this because, according to Section 1.6, we can only safely apply perturbation theory to the simultaneous eigenstates of the unperturbed and perturbing Hamiltonians.

Adopting the notation introduced in Section [s11.3], let \(\psi^{(2)}_{l,s;j,m_j}\) be a simultaneous eigenstate of \(L^2\), \(S^2\), \(J^{\,2}\), and \(J_z\) corresponding to the eigenvalues \[\begin{aligned} L^2\,\psi^{(2)}_{l,s;j,m_j} &= l\,(l+1)\,\hbar^{\,2}\,\psi^{(2)}_{l,s;j,m_j},\\[0.5ex] S^2\,\psi^{(2)}_{l,s;j,m_j} &= s\,(s+1)\,\hbar^{\,2}\,\psi^{(2)}_{l,s;j,m_j},\\[0.5ex] J^{\,2}\,\psi^{(2)}_{l,s;j,m_j} &= j\,(j+1)\,\hbar^{\,2}\,\psi^{(2)}_{l,s;j,m_j},\\[0.5ex] J_z\,\psi^{(2)}_{l,s;j,m_j} &= m_j\,\hbar\,\psi^{(2)}_{l,s;j,m_j}.\end{aligned}\] According to standard first-order perturbation theory, the energy-shift induced in such a state by spin-orbit coupling is given by \[\begin{aligned} {\mit\Delta} E_{l,1/2;j,m_j} &= \langle l,1/2;j,m_j|H_1|l,1/2;j,m_j\rangle\nonumber\\[0.5ex] &= \frac{e^{\,2}}{16\pi\,\epsilon_0\,m_e^{\,2}\,c^{\,2}}\left\langle 1,1/2;j,m_j\left|\frac{J^{\,2}-L^2-S^2}{r^{\,3}}\right|l,1/2;j,m_j\right\rangle\nonumber\\[0.5ex] &= \frac{e^{\,2}\,\hbar^{\,2}}{16\pi\,\epsilon_0\,m_e^{\,2}\,c^{\,2}}\,\left[j\,(j+1)-l\,(l+1)-3/4\right]\,\left\langle\frac{1}{r^{\,3}}\right\rangle.\end{aligned}\] Here, we have made use of the fact that \(s=1/2\) for an electron. It follows from Equation ([e9.75a]) that \[{\mit\Delta} E_{l,1/2;j,m_j}= \frac{e^{\,2}\,\hbar^{\,2}}{16\pi\,\epsilon_0\,m_e^{\,2}\,c^{\,2}\,a_0^{\,3}}\left[\frac{j\,(j+1)-l\,(l+1)-3/4}{l\,(l+1/2)\,(l+1)\,n^{\,3}}\right],\] where \(n\) is the radial quantum number. Finally, making use of Equations ([e9.55]), ([e9.56]), and ([e9.57]), the previous expression reduces to

\[\label{e12.137} {\mit\Delta} E_{l,1/2;j,m_j}= E_n\,\frac{\alpha^{\,2}}{n^{\,2}}\left[ \frac{n\,\left\{3/4+l\,(l+1)-j\,(j+1)\right\}}{2\,l\,(l+1/2)\,(l+1)}\right],\] where \(\alpha\) is the fine structure constant. A comparison of this expression with Equation ([e12.121]) reveals that the energy-shift due to spin-orbit coupling is of the same order of magnitude as that due to the lowest-order relativistic correction to the Hamiltonian. We can add these two corrections together (making use of the fact that \(j=l\pm 1/2\) for a hydrogen atom—see Section [s11.3]) to obtain a net energy-shift of

\[\label{e12.138} {\mit\Delta} E_{l,1/2;j,m_j}= E_n\,\frac{\alpha^{\,2}}{n^{\,2}}\left(\frac{n}{j+1/2}-\frac{3}{4}\right).\] This modification of the energy levels of a hydrogen atom due to a combination of relativity and spin-orbit coupling is known as *fine structure*.

Now, it is conventional to refer to the energy eigenstates of a hydrogen atom that are also simultaneous eigenstates of \(J^{\,2}\) as \(nL_j\) states, where \(n\) is the radial quantum number, \(L=(S,P,D,F,\cdots)\) as \(l=(0,1,2,3,\cdots)\), and \(j\) is the total angular momentum quantum number. Let us examine the effect of the fine structure energy-shift ([e12.138]) on these eigenstates for \(n=1,2\) and 3.

For \(n=1\), in the absence of fine structure, there are two degenerate \(1S_{1/2}\) states. According to Equation ([e12.138]), the fine structure induced energy-shifts of these two states are the same. Hence, fine structure does not break the degeneracy of the two \(1S_{1/2}\) states of hydrogen.

For \(n=2\), in the absence of fine structure, there are two \(2S_{1/2}\) states, two \(2P_{1/2}\) states, and four \(2P_{3/2}\) states, all of which are degenerate. According to Equation ([e12.138]), the fine structure induced energy-shifts of the \(2S_{1/2}\) and \(2P_{1/2}\) states are the same as one another, but are different from the induced energy-shift of the \(2P_{3/2}\) states. Hence, fine structure does not break the degeneracy of the \(2S_{1/2}\) and \(2P_{1/2}\) states of hydrogen, but does break the degeneracy of these states relative to the \(2P_{3/2}\) states.

For \(n=3\), in the absence of fine structure, there are two \(3S_{1/2}\) states, two \(3P_{1/2}\) states, four \(3P_{3/2}\) states, four \(3D_{3/2}\) states, and six \(3D_{5/2}\) states, all of which are degenerate. According to Equation ([e12.138]), fine structure breaks these states into three groups: the \(3S_{1/2}\) and \(3P_{1/2}\) states, the \(3P_{3/2}\) and \(3D_{3/2}\) states, and the \(3D_{5/2}\) states.

The effect of the fine structure energy-shift on the \(n=1\), 2, and 3 energy states of a hydrogen atom is illustrated in Figure below:

**Figure 23:***Effect of the fine structure energy-shift on theand 3 states of a hydrogen atom. Not to scale.*

Note, finally, that although expression ([e12.137]) does not have a well defined value for \(l=0\), when added to expression ([e12.121]) it, somewhat fortuitously, gives rise to an expression ([e12.138]) that is both well-defined and correct when \(l=0\) .

## Contributors and Attributions

Richard Fitzpatrick (Professor of Physics, The University of Texas at Austin)

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## FAQs

### What is fine structure in hydrogen? ›

The fine structure of the hydrogen atom is also known as the **hydrogen fine spectrum**. We know that the hydrogen atom is one of the simplest forms of atom available, which consists of a single electron in its valence shell.

**What is the fine structure of the hydrogen spectrum? ›**

Fine structure of hydrogen spectrum is explained by **spin angular momentum of electrons** whereas, orbital angular momentum, finite size of nucleus or the presence of neutrons in the nucleus does not explain the fine structure of hydrogen spectrum.

**What is the fine structure formula? ›**

The amount of splitting is characterized by a dimensionless constant called the fine-structure constant. This constant is given by the equation **α = ke ^{2}/hc**, where k is Coulomb's constant, e is the charge of the electron, h is Planck's constant, and c is the speed of light.

**What is fine structure of an atom? ›**

Fine structure describes the splitting of the spectral lines of atoms due to electron spin and relativistic corrections to the non-relativistic Schrödinger equation.

**What is fine structure number? ›**

Its name is the fine-structure constant, and it's a measure of the strength of the interaction between charged particles and the electromagnetic force. The current estimate of the fine-structure constant is **0.007 297 352 5693**, with an uncertainty of 11 on the last two digits.

**What is the value of the fine structure? ›**

Its numerical value is approximately **0.0072973525693 ≃ 1137.035999084**, with a relative uncertainty of 1.5×10^{−}^{10}. The constant was named by Arnold Sommerfeld, who introduced it in 1916 when extending the Bohr model of the atom.

**What is fine spectrum? ›**

Fine spectrum: **The splitting of the spectrum into tightly spaced lines** is known as the fine spectrum. When the H atom is exposed to an electrical or magnetic field, this spectrum is observed.

**What is the structure of the hydrogen atom? ›**

The hydrogen atom is the simplest of all atoms: it consists of **a single proton and a single electron**. In addition to the most common form of the hydrogen atom that is called protium, two other isotopes of hydrogen exist: deuterium and tritium.

**What is fine spectrum in chemistry? ›**

The fine structure or fine spectrum means **the splitting of spectral lines of an atom or molecule into two or more components**. Each component has different wavelengths. The fine structure is produced, when the making transition from one energy state to another energy state.

**What is fine structure analysis? ›**

Fine structure genetics encompasses **a set of tools used to examine not just the mutations within an entire genome, but can be isolated to either specific pathways or regions of the genome**. Ultimately, this more focused lens can lead to a more nuanced and interactive view of the function of a gene.

### What is fine-structure constant in simple terms? ›

The fine structure constant, α, can be thought of as the ratio between the energy needed to overcome the electrostatic repulsion driving these electrons apart and the energy of a single photon whose wavelength is 2π multiplied by the separation between those electrons.

**How is the fine-structure constant measured? ›**

In particular, the fine-structure constant is a crucial parameter for testing quantum electrodynamics (QED) and the standard model. This test relies on the comparison between the measured value of the electron gyromagnetic anomaly **a _{e} = (g_{e} − 2)/2 (where g_{e} is the electron g factor) and its theoretical value**.

**Where is the fine-structure constant? ›**

Numerically, the fine-structure constant, denoted by the Greek letter α (alpha), comes very close to the ratio 1/137. It **commonly appears in formulas governing light and matter**.

**Where is the structure of an atom? ›**

Atoms are made up of protons and neutrons located **within the nucleus**, with electrons in orbitals surrounding the nucleus. The hydrogen atom (H) contains only one proton, one electron, and no neutrons.

**Can you explain the structure of an atom? ›**

**Atoms consist of an extremely small, positively charged nucleus surrounded by a cloud of negatively charged electrons**. Although typically the nucleus is less than one ten-thousandth the size of the atom, the nucleus contains more that 99.9% of the mass of the atom.

**What is the fine structure of carbon? ›**

For carbon, the fine structure lines are forbidden lines and are listed as **[CI] (490 GHz and 810 GHz) and [CII] (1.9 THz) for neutral and ionized carbon**. Oxygen fine structure lines include 63 μm.

**What is the difference between fine structure and gross structure? ›**

In atomic physics, the fine structure describes the splitting of the spectral lines of atoms. The gross structure of line spectra is due to the principal quantum number n, giving the main electron shells of atoms.

**What is fine and hyperfine structure? ›**

The fine structure comes from the spin-orbit, spin-other-orbit, and spin-spin interactions. The hyperfine structure of atomic energy levels is caused by the interaction between the electrons and the electromagnetic multipole moments of the nucleus.

**Why is fine-structure important? ›**

The fine-structure constant **determines the strength of the electromagnetic force**, and is central in explaining a number of phenomena including the interactions between light and charged elementary particles such as electrons.

**What does fine-structure mean in biology? ›**

fine structure. noun. : **microscopic structure of a biological entity or one of its parts especially as studied in preparations for the electron microscope**.

### Why 137 is the most magical number? ›

To physicists, 137 is the approximate denominator of the fine-structure constant (1/137.03599913), the measure of the strength of the electromagnetic force that controls how charged elementary particles such as the electron and muon interact with photons of light, according to the National Institute of Standards and ...

**What is the H alpha line of hydrogen? ›**

H-alpha (Hα) is **a deep-red visible spectral line of the hydrogen atom with a wavelength of 656.28 nm in air and 656.46 nm in vacuum**.

**What type of structure is H2? ›**

Dihydrogen is **an elemental molecule consisting of two hydrogens joined by a single bond**. It has a role as an antioxidant, an electron donor, a fuel, a human metabolite and a member of food packaging gas. It is an elemental hydrogen, a gas molecular entity and an elemental molecule.

**What are the 3 atoms of hydrogen? ›**

**Hydrogen-3 (tritium)**

A tritium atom contains one proton, two neutrons, and one electron.

**What type of structure is a hydrogen bond? ›**

Hydrogen Bonding. Hydrogen bonding is a special type of **dipole-dipole attraction** between molecules, not a covalent bond to a hydrogen atom.

**What is an example of a spectrum? ›**

A natural example of a spectrum is **a rainbow**. The word spectrum was first used by scientists studying optics. They used the word to describe the rainbow of colors in visible light when separated using a prism.

**Are there two types of spectrum? ›**

This is called spectrum. The spectra can be divided into two types viz., **emission and absorption spectra**.

**What is a spectrum of an atom? ›**

Atomic spectra are defined as. **The spectrum of the electromagnetic radiation emitted or absorbed by an electron during transitions between different energy levels within an atom**. When an electron gets excited from one energy level to another, it either emits or absorbs light of a specific wavelength.

**What is fine structure mapping? ›**

The goal of fine structure mapping is **to develop complete contig maps for each chromosome of the species**. If these complete maps are available, it is a simple matter to take the molecular marker you have obtained and select a clone to which it hybridized.

**What is fine structure 137? ›**

The fine-structure constant α is of dimension 1 (i.e., it is simply a number) and **very nearly equal to 1/137**. It is the "coupling constant" or measure of the strength of the electromagnetic force that governs how electrically charged elementary particles (e.g., electron, muon) and light (photons) interact.

### What is fine structure in English? ›

fine structure. noun. **the splitting of a spectral line into two or more closely spaced components as a result of interaction between the spin and orbital angular momenta of the atomic electrons**Compare hyperfine structure.

**Does the fine-structure constant vary? ›**

Fine structure constant **may vary with space, constant in time**.

**What is the fine-structure constant for gravity? ›**

Relativistic effects are shown to be suppressed by the gravitational fine-structure constant **αG=Gm1m2/(ℏc)**, where G is Newton's gravitational constant, c is the speed of light, and m1 and m2≫m1 are the masses of the two particles.

**What fraction is the fine-structure constant? ›**

The fine structure constant, a number that emerges from theories of quantum mechanics, is measured in laboratory experiments to be roughly **1/137**. This slightly coincidental number is a perennial source of excitement.

**What is the most accurate measurement of the fine-structure constant? ›**

The most accurate measurement to date – of **1/137.03599920611**, with an uncertainty of 81 parts per trillion – was made by using the recoil of rubidium atoms when struck by photons to measure the atoms' mass.

**What is the fine-structure constant and the golden ratio? ›**

The Fine-structure constant and the Golden ratio are **two sides of the same coin**. Pi is found in the angle and amount of space between Alpha and Phi. So in the same way the Golden ratio governs how things grow, the Fine-structure constant governs how things stick together, while Pi seems to control the space between.

**What is the nature fine-structure constant? ›**

Every physicist knows the approximate value (1/137) of a fundamental constant called the fine-structure constant, α. This constant **describes the strength of the electromagnetic force between elementary particles in the standard model of particle physics** and is therefore central to the foundations of physics.

**What is the fine surface constant? ›**

The fine structure constant is **a ratio of geometric surface areas**. It can be used to calculate wave amplitude as it transitions from one geometry to another – specifically spherical to a one-dimensional vibration.

**What is an atom made of? ›**

There are three subatomic particles: **protons, neutrons and electrons**. Two of the subatomic particles have electrical charges: protons have a positive charge while electrons have a negative charge. Neutrons, on the other hand, don't have a charge.

**How atoms are formed? ›**

Atoms are composed of a nucleus in the center containing protons, neutrons, and electrons surrounding the nucleus. Atoms are formed **by the fission process of Uranium into smaller atoms**. The Big Bang and Supernova events are real-life examples of the formation of atoms in a vast quantity.

### Are all atoms the same? ›

But, **all atoms are not the same**. You know that the number of protons in an atom determines what element you have. For instance hydrogen has one proton, carbon has six. The difference in the number of protons and neutrons in atoms account for many of the different properties of elements.

**Are humans made of atoms? ›**

**About 99 percent of your body is made up of atoms of hydrogen, carbon, nitrogen and oxygen**. You also contain much smaller amounts of the other elements that are essential for life.

**How big is atom? ›**

The atoms are very small that they can not be seen through naked eyes. An electron microscope is needed to watch an atom. The diameter of an atom is in the range of **0.1nm to 0.5nm**.

**What are the two main parts of the atom? ›**

Key Points

An atom is composed of two regions: **the nucleus, which is in the center of the atom and contains protons and neutrons, and the outer region of the atom, which holds its electrons in orbit around the nucleus**.

**What does fine structure mean in biology? ›**

fine structure. noun. : **microscopic structure of a biological entity or one of its parts especially as studied in preparations for the electron microscope**.

**What is meant by fine structure and hyperfine structure of hydrogen atom? ›**

The key difference between fine and hyperfine structure is that in fine structures, the line splitting is a result of the energy changes that are produced by electron spin-orbit coupling, whereas in hyperfine structures, the line splitting is a result of the interaction between the magnetic field and nuclear spin.

**What is fine vs hyperfine structure? ›**

The fine structure comes from the spin-orbit, spin-other-orbit, and spin-spin interactions. The hyperfine structure of atomic energy levels is caused by the interaction between the electrons and the electromagnetic multipole moments of the nucleus.

**What is meant by fine structure of alpha decay? ›**

The α fine-structure was discovered by Rosenblum [1] since 1929 by **measuring the range of emitted particle in air**. It reveals the essential variation of particle emission probability for different states of daughter nucleus.

**Why is fine structure important? ›**

The fine-structure constant **determines the strength of the electromagnetic force**, and is central in explaining a number of phenomena including the interactions between light and charged elementary particles such as electrons.

**What is the structure of a hydrogen atom explain? ›**

A hydrogen atom is an atom of the chemical element hydrogen. The electrically neutral atom **contains a single positively charged proton and a single negatively charged electron bound to the nucleus by the Coulomb force**. Atomic hydrogen constitutes about 75% of the baryonic mass of the universe.

### What is the hyper fine level? ›

The hyperfine levels of the spectral line **describe the splitting of spectral lines due to the electron spin and the relativistic correction to the total energy of the hydrogen atom electron**.

**What is the history of fine structure? ›**

The fine-structure constant was **introduced in 1916** to quantify the tiny gap between two lines in the spectrum of colors emitted by certain atoms. The closely spaced frequencies are seen here through a Fabry-Pérot interferometer. Computational Physics Inc.

**What is an example of a hyperfine structure? ›**

Small molecule hyperfine structure

A typical simple example of the hyperfine structure due to the interactions discussed above is in the **rotational transitions of hydrogen cyanide ( ^{1}H^{12}C^{14}N) in its ground vibrational state**.

**What is the most accurate measurement of fine-structure constant? ›**

The most accurate measurement to date – of **1/137.03599920611**, with an uncertainty of 81 parts per trillion – was made by using the recoil of rubidium atoms when struck by photons to measure the atoms' mass.

**What is the value of fine-structure constant alpha? ›**

The fine-structure constant α is of dimension 1 (i.e., it is simply a number) and very nearly equal to **1/137**. It is the "coupling constant" or measure of the strength of the electromagnetic force that governs how electrically charged elementary particles (e.g., electron, muon) and light (photons) interact.

**What is alpha decay vs gamma decay? ›**

Unlike alpha and beta particles, which have both energy and mass, **gamma rays are pure energy**. Gamma rays are similar to visible light, but have much higher energy. Gamma rays are often emitted along with alpha or beta particles during radioactive decay. Gamma rays are a radiation hazard for the entire body.

**What is alpha decay quizlet? ›**

alpha decay. **A nuclear reaction in which an atom loses two protons and two neutrons**. This decreases the atomic number by 2 and the mass number by 4.