Structure Of The Atom (Early Models)

Charged Particles In Matter

Dalton's atomic theory proposed that atoms were indivisible. However, towards the end of the 19th century, scientists like Michael Faraday began studying the passage of electricity through substances, leading to the discovery of sub-atomic particles. These discoveries indicated that atoms are, in fact, divisible and contain smaller, charged particles.

One of the most significant experiments that revealed the presence of charged particles was the study of the discharge of electricity through gases at very low pressures, using cathode ray tubes.

Discovery of Electrons (Cathode Rays)

In 1897, J.J. Thomson performed experiments using a cathode ray tube. A cathode ray tube is a sealed glass tube with two electrodes, a cathode (negative) and an anode (positive), connected to a high voltage source. When voltage is applied at very low pressure inside the tube, a stream of particles travels from the cathode to the anode, producing a glow on the glass wall behind the anode. These were called cathode rays.

Thomson studied the properties of these cathode rays by applying electric and magnetic fields. He observed that:

• Cathode rays travel in straight lines.
• They are deflected by electric and magnetic fields in a direction indicating that they carry a negative charge.
• The properties of cathode rays were the same regardless of the material of the cathode or the gas in the tube, suggesting that these negatively charged particles are fundamental constituents of all matter.

Thomson measured the charge-to-mass ratio ($e/m$) of these particles and found it to be constant. He called these particles electrons.

The electron is a fundamental sub-atomic particle with a negative charge (standard charge, $e = 1.602 \times 10^{-19}$ C) and a very small mass (approx. 9.109 $\times 10^{-31}$ kg), which is about $1/1837$th the mass of a hydrogen atom.

Discovery of Protons (Anode Rays / Canal Rays)

Shortly after the discovery of electrons, experiments with modified discharge tubes (with a perforated cathode) led to the discovery of positively charged particles. In 1886, E. Goldstein observed a new set of rays, called canal rays (or anode rays), streaming through the perforations of the cathode towards the cathode.

These rays consisted of positively charged particles. Unlike cathode rays, the properties of anode rays (specifically, their charge-to-mass ratio) were found to depend on the gas present in the discharge tube. The simplest positive ions were produced when Hydrogen gas was used, resulting in particles with the smallest positive charge and mass.

These positively charged particles were later identified as protons by Ernest Rutherford. The proton is a fundamental sub-atomic particle with a positive charge equal in magnitude to the electron's negative charge ($+e$) and a mass approximately equal to the mass of a hydrogen atom (approx. 1.672 $\times 10^{-27}$ kg), which is about 1837 times the mass of an electron.

These discoveries of electrons and protons demonstrated that atoms are not indivisible but are composed of charged sub-atomic particles. This necessitated the development of models to describe how these particles are arranged within an atom.

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The Structure Of An Atom

Following the discovery of electrons and protons, the question arose: how are these tiny charged particles arranged within an atom to make it electrically neutral?

Since atoms are electrically neutral, the total positive charge must be equal to the total negative charge. Various models were proposed to explain the structure of the atom.

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Thomson’s Model Of An Atom

In 1903, J.J. Thomson proposed the first model for the structure of an atom, often called the Plum Pudding Model or Raisin Pudding Model.

Postulates of Thomson's Model:

1. An atom consists of a uniformly distributed sphere of positive charge.
2. The electrons (negative charges) are embedded within this sphere of positive charge, like plums in a pudding or raisins in a spherical sweet.
3. The total positive charge in the sphere is equal in magnitude to the total negative charge of the electrons, so the atom as a whole is electrically neutral.

Thomson's model explained the electrical neutrality of the atom. However, it did not have strong experimental support and was later contradicted by experimental results.

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Rutherford’s Model Of An Atom

In 1911, Ernest Rutherford and his students (Hans Geiger and Ernest Marsden) conducted a landmark experiment that revolutionised the understanding of atomic structure. This was the alpha ($\alpha$) particle scattering experiment.

Experimental Setup: A beam of highly energetic alpha particles (which are positively charged helium nuclei, He$^{2+}$) from a radioactive source was directed at a very thin gold foil (about 1000 atoms thick). A fluorescent screen was placed around the gold foil to detect the deflected alpha particles by the flashes of light they produced.

Observations: Rutherford expected, based on Thomson's model (where positive charge is spread out), that the alpha particles would pass straight through the foil or be only slightly deflected.

However, the actual observations were startling:

1. Most (about 99%) of the alpha particles passed straight through the gold foil without any deflection.
2. Some alpha particles were deflected by small angles.
3. A very few alpha particles (about 1 in 12,000) were deflected by large angles, or even bounced back ($> 90^\circ$, some nearly $180^\circ$). This unexpected observation led Rutherford to famously remark that it was "about as incredible as if you fired a 15-inch shell at a piece of tissue paper and it came back and hit you".

Conclusions from Observations: Based on these observations, Rutherford proposed his Nuclear Model of the Atom:

1. Mostly Empty Space: Since most alpha particles passed straight through, it indicates that most of the space within an atom is empty.
2. Presence of a Small, Dense, Positively Charged Centre: The small fraction of alpha particles deflected at large angles must have experienced a strong repulsive force. This force could only be exerted by a concentration of positive charge in a very small volume within the atom. Rutherford called this positively charged centre the nucleus. The deflection of particles suggested that the positive charge and most of the mass of the atom are concentrated in this tiny nucleus.
3. Electrons Orbit the Nucleus: The electrons (negatively charged) revolve around the nucleus in well-defined paths called orbits. Since the mass of electrons is negligible compared to alpha particles, they would not cause significant deflection.
4. Atom is Electrically Neutral: The total negative charge of the electrons is equal to the total positive charge of the nucleus, making the atom electrically neutral.
5. Size of the Nucleus: Rutherford estimated that the size of the nucleus is very small compared to the size of the atom. The radius of the nucleus is about $10^{-15}$ m, while the radius of the atom is about $10^{-10}$ m. This means the nucleus occupies only about $10^{-15}$ times the volume of the atom.

Rutherford's model was a major improvement over Thomson's model. It correctly explained the alpha particle scattering experiment and introduced the concept of the nucleus.

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Drawbacks Of Rutherford’s Model Of The Atom

Despite its success, Rutherford's nuclear model had significant limitations:

1. Stability of the Atom: According to classical electromagnetic theory, an electron moving in a circular orbit around the nucleus is an accelerating charged particle. An accelerating charged particle is expected to continuously radiate energy. If an electron loses energy continuously, its orbit should become smaller and smaller, and it should eventually spiral into the nucleus. If this happened, the atom would collapse, and matter would not be stable. However, atoms are generally stable. Rutherford's model could not explain this stability.
2. Explanation of Atomic Spectra: Rutherford's model predicted that electrons could revolve in any orbit of any radius, and their continuous energy loss would lead to a continuous spectrum of emitted light. However, experimentally observed atomic spectra are line spectra, meaning atoms emit and absorb light only at specific, discrete wavelengths. Rutherford's model could not explain this discrete nature of atomic spectra.

These drawbacks indicated that classical physics could not fully explain the behaviour of electrons within an atom, paving the way for quantum mechanics and new atomic models.

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Bohr’s Model Of Atom

In 1913, Niels Bohr, a student of Rutherford, proposed a new model for the hydrogen atom, incorporating concepts from quantum theory to overcome the drawbacks of Rutherford's model.

Postulates of Bohr's Model (for the Hydrogen Atom):

1. Electrons orbit in specific stable orbits or stationary states: Electrons revolve around the nucleus only in certain specific, stable orbits without radiating energy. These orbits are called stationary states or energy levels.
2. Electrons do not radiate energy in stationary orbits: While revolving in these specific orbits, the electron's energy remains constant. This addressed the stability problem of Rutherford's model.
3. Energy is emitted or absorbed only during transitions: Electrons can jump from one stationary orbit to another. Energy is absorbed when an electron moves from a lower energy level to a higher energy level (excitation). Energy is emitted when an electron moves from a higher energy level to a lower energy level (de-excitation). The energy difference between the two levels is emitted or absorbed as a photon of light.

$ \Delta E = E_{\text{higher}} - E_{\text{lower}} = h\nu $

Where $\Delta E$ is the energy difference, $h$ is Planck's constant ($6.626 \times 10^{-34}$ J s), and $\nu$ is the frequency of the emitted or absorbed photon.

4. Quantisation of Angular Momentum: The angular momentum of an electron in a stationary orbit is quantised. It is an integral multiple of $\frac{h}{2\pi}$.

$ L = m_e v r = n \frac{h}{2\pi} $

Where $m_e$ is the mass of the electron, $v$ is its velocity, $r$ is the radius of the orbit, $n$ is a positive integer (1, 2, 3, ...), and $n$ is called the principal quantum number. This postulate implies that only orbits with specific radii and energies are allowed.

Explanation of Stability and Spectra by Bohr's Model:

• The postulate that electrons do not radiate energy in stationary orbits explained the stability of the atom.
• The postulate that energy is emitted/absorbed only during transitions between discrete energy levels explained the origin of line spectra. Each line in the spectrum corresponds to a specific energy difference between two allowed orbits.

Bohr successfully calculated the radii of the allowed orbits and the energy of the electron in each orbit for the hydrogen atom:

Radius of the $n^{th}$ orbit ($r_n$):

$ r_n = (0.0529 \text{ nm}) n^2 = (52.9 \text{ pm}) n^2 $

Energy of the electron in the $n^{th}$ orbit ($E_n$):

$ E_n = -\frac{R_H}{n^2} = -\frac{2.18 \times 10^{-18} \text{ J}}{n^2} = -\frac{13.6 \text{ eV}}{n^2} $

Where $R_H$ is the Rydberg constant in energy units, and $n=1, 2, 3, \dots$ are the principal quantum numbers. The negative sign indicates that the electron is bound to the nucleus. $n=1$ is the lowest energy level (ground state), and higher values of $n$ correspond to higher energy levels (excited states).

Bohr's model successfully calculated the wavelengths of the spectral lines of hydrogen, matching experimental values. It also provided a basis for understanding the energy levels of atoms.

Limitations of Bohr's Model:

• It could only explain the spectrum of hydrogen and hydrogen-like species (containing only one electron, e.g., He$^+$, Li$^{2+}$). It failed for multi-electron atoms.
• It did not explain the fine structure of spectral lines (splitting of lines into closely spaced lines under high resolution).
• It did not explain the Zeeman effect (splitting of spectral lines in a magnetic field) and the Stark effect (splitting of spectral lines in an electric field).
• It treated the electron as a particle revolving in definite orbits, which is not consistent with the wave nature of electrons and Heisenberg's Uncertainty Principle (from quantum mechanics).

Despite limitations, Bohr's model was a crucial step in applying quantum theory to atomic structure and laid the groundwork for more advanced quantum mechanical models.

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Neutrons

Even after Rutherford and Bohr's models, there was a discrepancy between the atomic mass calculated from protons and the experimentally determined atomic mass for many elements. For example, Helium has 2 protons (mass $\approx$ 2 amu), but its atomic mass is $\approx$ 4 amu.

This led to the prediction of a neutral particle in the nucleus. In 1932, James Chadwick discovered this particle, which he called the neutron.

Discovery: Chadwick bombarded Beryllium with alpha particles and observed the emission of a new type of radiation that was highly penetrating but not deflected by electric or magnetic fields, indicating it was electrically neutral. The mass of these particles was found to be slightly greater than that of a proton.

The neutron is a sub-atomic particle with no electric charge and a mass approximately equal to that of a proton (approx. 1.675 $\times 10^{-27}$ kg).

Structure of the Atom (Current understanding based on early models): An atom consists of a tiny, dense nucleus located at the centre, containing protons (positively charged) and neutrons (neutral). These particles are collectively called nucleons. The nucleus contains almost all the mass of the atom. Electrons (negatively charged) revolve around the nucleus in specific energy levels or shells. The number of protons determines the element (atomic number, Z). In a neutral atom, the number of electrons equals the number of protons. The mass number (A) is the total number of protons and neutrons in the nucleus ($A = Z + N$, where N is the number of neutrons).

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How Are Electrons Distributed In Different Orbits (Shells)?

Bohr's model introduced the concept of discrete energy levels or shells where electrons orbit the nucleus. These energy levels are designated by principal quantum numbers, $n=1, 2, 3, \dots$. These are also often referred to as shells and are labelled as K, L, M, N, ... shells, corresponding to $n=1, 2, 3, 4, \dots$ respectively.

The distribution of electrons in these different shells is called the electronic configuration of an atom. This distribution follows certain rules, commonly known as the Bohr-Bury rules (or rules for filling electrons in shells), which were proposed by Niels Bohr and E. Bury.

Rules for filling electrons in shells:

1. The maximum number of electrons that can be accommodated in a shell is given by the formula $2n^2$, where $n$ is the principal quantum number of the shell.
   • For the first shell (K, $n=1$): Maximum capacity = $2 \times 1^2 = 2$ electrons.
   • For the second shell (L, $n=2$): Maximum capacity = $2 \times 2^2 = 8$ electrons.
   • For the third shell (M, $n=3$): Maximum capacity = $2 \times 3^2 = 18$ electrons.
   • For the fourth shell (N, $n=4$): Maximum capacity = $2 \times 4^2 = 32$ electrons, and so on.
2. Electrons are not filled in a shell unless the inner shells are completely filled. Shells are filled in a step-wise manner from the innermost shell (K shell) outwards.
3. The outermost shell of an atom cannot accommodate more than 8 electrons (octet rule, with exceptions).
4. The second last shell (penultimate shell) cannot accommodate more than 18 electrons. (This rule becomes more relevant for elements beyond Calcium).

These rules provide a simple way to determine the electronic configuration of elements, especially for the first few periods of the periodic table. The number of electrons in the outermost shell is called the valence electrons, which largely determine the chemical properties of the element.

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While these rules are helpful for understanding the electronic configuration of the first few elements, the filling pattern becomes more complex for heavier elements, involving subshells (s, p, d, f) within each main shell, which is explained by the Aufbau principle, Hund's rule, and Pauli's exclusion principle in more advanced studies.

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