Atoms and Nuclei

Atoms are made of a nucleus (protons and neutrons) and electrons. Models like Thomson's, Rutherford's, Bohr's, and the quantum model explain atomic structure. The atomic number (Z) defines an element, and isotopes differ by neutrons. Nuclear reactions like fission and fusion release energy, while radioactivity involves the emission of alpha, beta, or gamma particles from unstable nuclei. These processes are crucial in energy, medicine, and physics.

1.0Various Models for Structure of Atom

Dalton's Atomic Theory

• This theory states that all matter is composed of indivisible atoms, which cannot be created or destroyed. Atoms of the same element are identical in properties, while those of different elements have distinct properties. Atoms of different elements are made up of hydrogen atoms, with heavier atoms being larger and more massive. Atoms are stable and electrically neutral.(The radius of the heaviest atom is about 10 times that of a hydrogen atom and its mass is about 250 times that of hydrogen).

Thomson's Atom Model

• The atom is electrically neutral, with the positive charge equal to the negative charge of electrons.
• It is a positively charged sphere (radius 10⁻¹⁰ m) with electrons embedded within.
• The positive charge and mass are uniformly distributed.

Shortcomings:

1. Cannot explain the atomic spectrum.
2. Cannot explain the scattering of α-particles.

Rutherford atomic model

Rutherford's Experiment on α-Particle Scattering:

• Conducted by Rutherford, Geiger, and Marsden.
• A beam of α-particles (5.5 MeV) from a Bi-214 radioactive source was directed at a thin gold foil.
• The setup included a lead box with a small hole for collimated α-particles, along with a movable zinc sulfide screen to detect scattered α-particles. When α-particles hit the screen, they create flashes of light, allowing the angles of scattering to be observed."

Key Findings:

• The majority of alpha particles passed directly through the gold foil, suggesting that atoms are largely composed of vacant space.
• A few α-particles were deflected at large angles, some even reversing direction.
• The positive charge and almost all the mass are focused in a small central nucleus.
• Electrons, being very light, did not deflect α-particles.
• Electrons rotate around the nucleus in circular orbits.
• The atom has a dense nucleus at its center (diameter < 10⁻¹³ cm).
• Rutherford's scattering formula describes the number of α-particles scattered at different angles.
• This central core, now called nucleus, is surrounded by clouds of electrons that makes the entire atom electrically neutral.

Failure of Rutherford's Atomic model

(1) It failed to  explain the stability of atoms.

(2) It could not explain the discrete nature of hydrogen spectra.

2.0Bohr Model of Hydrogen Atom

1.Electron Movement: An electron moves in a circular orbit around the nucleus, influenced by Coulomb's force of attraction between the electron and the nucleus. This force also provides the necessary centripetal force.

$\frac{m{v}^2}{r}=\frac{e^2}{4\pi {ϵ}_0{r}^2}$

2.Quantized Orbits: The electron can only occupy orbits where its angular momentum is an integer multiple of a specific value of h2​ are allowed.

$mvr=n(\frac{h}{2\pi })$ where n is a positive integer and h is Planck's constant.

3.Stationary Orbits: Electrons in these allowed orbits do not emit radiation, and their energy remains constant.

4.Emission of Radiation: When an electron jumps from a higher energy orbit (E2) to a lower energy orbit (E1), electromagnetic radiation is emitted. The frequency () of the released radiation is given by:

$E_2-E_1=h\nu$

Drawbacks of Bohr's Model:

1. Could not explain the fine structure of spectral lines, Zeeman effect, and Stark effect.
2. Only valid for single-electron systems, not explaining electron-electron interactions.
3. Based on circular orbits, which don't exist in reality.
4. Assumed electrons revolve around the nucleus, but electron motion can't be described simply.
5. Could not explain the intensity of spectral lines.
6. Failed to explain doublets in spectra of some atoms.
7. It's a semi-quantum model, considering only two quantum numbers and assuming circular electron motion.

3.0Electron energy levels in hydrogen atom

• The energy level diagram shows the lowest energy level (n = 1) as the ground state of hydrogen.
• Lower (more negative) energies are at the bottom, and higher (less negative) energies are at the top.
• Electron transitions are represented by vertical arrows between energy levels.
• The energy of the emitted photon increases with the length of the arrow.

4.0Nucleus and Types of Nuclei

• The Nucleus is a central core of every atom discovered by Rutherford in scattering experiment.
• Order of nuclear size=10^-15m and of atomic size=10^-10 m
• Atomic mass is expressed by atomic mass unit (u)
• 1u=1.66✖10^-27 kg

5.0Einstein's Mass - Energy Relation

According to Einstein, mass can be converted into energy and energy into mass.

$E=m{c}^2$

Here, E = total energy associated with mass m

$c^2$ = used as a conversion coefficient

6.0Nuclear Forces and its Properties

• The most robust interaction holding nucleons together to form nuclei is strong enough to overcome the electric repulsion of protons and neutrons.
• The most vital force in the universe.
• Works only between the nucleons
• Very short range force
• It depends on distance
• Charge independent
• Spin dependent 
• Non central force
• Nature-(1) Attractive-distance greater than 0.8 fm 

             (2) Repulsive-distance lesser than 0.8 fm.

7.0Binding Energy per Nucleon Curve

• The value of binding energy per nucleon decides the stability of the nucleus
• A nucleus becomes more stable as the binding energy per nucleon increases.
• The maximum for Iron( Fe) is 8.8 Mev, the most stable nucleus.
• For Uranium 7.7Mev it is unstable
• Medium- sized nuclei are more stable than light or heavy nuclei.

8.0Difference between Nuclear Fission and Nuclear Fusion

9.0Required Condition For Nuclear Fusion

• High Temperature
• High Pressure(Density)

10.0Pair Production and Pair Annihilation

Pair Production:

• This occurs when a high-energy photon (gamma ray) interacts with a strong electromagnetic field (usually near a nucleus) and transforms into a particle-antiparticle pair.
• For example, a photon can produce an electron and a positron: $\gamma \Rightarrow e^{-}+e^{+}$
• The energy of the photon must exceed the combined rest mass energy of the two particles (1.022 MeV) for pair production to occur.

Pair Annihilation:

• This is the reverse process, where a particle and its corresponding antiparticle (e.g., electron and positron) collide and annihilate each other.
• The result is the conversion of their mass into energy, typically in the form of two photons $e^{-}+e^{+}\Rightarrow \gamma +\gamma$
• The energy of the annihilation is typically 1.022 MeV (the combined rest mass of the electron and positron).
  

In Nuclear Fission

$ReproductionFactor(K)=\frac{RateofProductionofneutrons}{RateofLossofneutrons}$

• K=1,a chain reaction will be steady or sustained.
• K>1, supercritical this will result in an explosion
• K<1,Sub critical chain reaction will retard and ultimately stops

11.0Radioactivity and Types of Process

• Radioactivity is a process of spontaneous emission of radiation from the nucleus; only unstable nuclei exhibit this property.

12.0Difference Between Alpha($\alpha$), Beta($\beta$) and Gamma($\gamma$) Decay process

13.0K-Electron Capture and Artificial Transmission

• In K-capture a nucleus captures one of the inner orbital electrons and a proton transforms into a neutron.
• Hence K capture is like positron decay, in both n/p ratio increases. In this event a vacancy is created in K-shell to fill up the vacancy, electron transition takes place and X-rays are emitted.