Charged Particles In Matter

Simple experiments involving static electricity suggest the presence of charged particles within matter. For example, rubbing a comb through dry hair causes the comb to attract small pieces of paper, and rubbing a glass rod with silk makes it attract a balloon. This indicates that friction can transfer electrical charges between objects.

The source of these charges implies that atoms themselves are not electrically neutral particles as a whole, but rather contain charged constituents.

By around 1900, despite the prevailing view of atoms as indivisible, it became clear they contained smaller particles.

• Electrons (e⁻): Discovered by J.J. Thomson. These are negatively charged sub-atomic particles. They have a very small mass, considered negligible compared to protons and neutrons (about 1/2000th the mass of a hydrogen atom). Their charge is taken as -1 unit. Electrons are relatively easy to remove from atoms.
• Protons (p⁺): Discovered by E. Goldstein through experiments with gas discharges using 'canal rays' (streams of positively charged particles). Protons are positively charged sub-atomic particles. Their charge is equal in magnitude but opposite in sign to that of an electron (+1 unit). The mass of a proton is approximately 2000 times that of an electron, and is taken as 1 atomic mass unit (u). Protons reside within the atom's core and are not easily removed.

Initial understanding suggested atoms were composed of equal numbers of protons and electrons, balancing their charges to make the atom electrically neutral overall. The key question then became how these particles were arranged within the atomic structure.

The Structure Of An Atom

The discovery of electrons and protons contradicted Dalton's idea of the atom as an indivisible and indestructible particle. This necessitated new models to explain the arrangement of these sub-atomic particles within the atom.

J.J. Thomson proposed the first formal model for the structure of an atom.

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Thomson’s Model Of An Atom

Thomson's model is often compared to a Christmas pudding or a watermelon.

Key Postulates of Thomson's Model:

1. An atom consists of a uniformly positively charged sphere.
2. The electrons (negative charges) are embedded within this positive sphere, like plums in a pudding or seeds in a watermelon.
3. The total positive charge of the sphere is equal in magnitude to the total negative charge from the electrons. This ensures that the atom as a whole is electrically neutral.

Thomson's model successfully explained the overall electrical neutrality of atoms. However, it failed to explain the results of later experiments conducted by other scientists, particularly Rutherford's alpha-particle scattering experiment.

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Rutherford’s Model Of An Atom

Ernest Rutherford, a student of J.J. Thomson, sought to understand the arrangement of electrons by conducting the famous alpha-particle scattering experiment.

Experimental Setup: Fast-moving alpha ($\alpha$) particles (which are positively charged helium ions, He²⁺, with a mass of 4 u) were directed towards a very thin sheet of gold foil (approximately 1000 atoms thick). A fluorescent screen was placed around the foil to detect the deflection of the $\alpha$-particles.

Rutherford expected the massive $\alpha$-particles to pass straight through the foil or be deflected only slightly by the sub-atomic particles within the gold atoms, as per Thomson's model.

Unexpected Observations:

1. Most (about 99.9%) of the fast $\alpha$-particles passed straight through the gold foil without any deflection.
2. A small fraction of the $\alpha$-particles were deflected by small angles.
3. A very small number (about 1 in 12,000) of the $\alpha$-particles were deflected by large angles or even appeared to rebound almost back towards the source (deflection of 180$^\circ$).

Rutherford described the rebounding of $\alpha$-particles as "almost as incredible as if you fire a 15-inch shell at a piece of tissue paper and it comes back and hits you."

Conclusions Drawn from Observations: Based on these unexpected results, Rutherford made the following conclusions, reasoning much like a blindfolded child throwing stones at a wall vs. a barbed-wire fence:

1. The fact that most $\alpha$-particles passed straight through indicated that most of the space inside an atom is empty.
2. The deflection of some $\alpha$-particles suggested that there is a small, positively charged region within the atom that repelled the positive $\alpha$-particles. This positive charge must occupy very little volume.
3. The occasional large-angle deflection or rebound implied that the entire positive charge and almost all the mass of the atom are concentrated in a very small volume at the centre.

Based on his experiment, Rutherford proposed the Nuclear Model of the Atom.

Features of Rutherford’s Nuclear Model:

1. There is a positively charged centre in the atom called the nucleus. Nearly all the mass of the atom is concentrated in the nucleus.
2. The electrons revolve around the nucleus in well-defined circular paths (orbits).
3. The size of the nucleus is very small compared to the overall size of the atom. Rutherford calculated that the radius of the nucleus is about $10^5$ times smaller than the radius of the atom.

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Drawbacks Of Rutherford’s Model Of The Atom

Despite introducing the concept of a nucleus, Rutherford's model faced significant challenges regarding the stability of the atom.

According to classical physics, a charged particle in circular motion (like an electron revolving around the nucleus) undergoes acceleration. An accelerating charged particle is expected to radiate energy continuously.

If the orbiting electrons continuously lost energy, they would spiral inwards and eventually fall into the nucleus. This would cause the atom to collapse, making it highly unstable.

However, we know that atoms are generally very stable and do not collapse. Rutherford's model could not explain this stability of the atom, which was a major limitation.

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Bohr’s Model Of Atom

To address the stability problem of Rutherford's model, Neils Bohr proposed a modified model of the atom incorporating some quantum mechanical concepts.

Postulates of Bohr's Model:

1. Only certain special orbits, known as discrete orbits or stationary states, are allowed for electrons inside the atom. Electrons can only revolve in these specific orbits.
2. While revolving in these discrete orbits, the electrons do not radiate energy. This explains why the atom is stable and the electrons don't spiral into the nucleus.

These allowed orbits are also referred to as energy levels or shells. They are represented by letters K, L, M, N, ... or by numbers n = 1, 2, 3, 4, ... starting from the nucleus (n=1 corresponds to the K shell).

Electrons gain or lose energy only when they move from one energy level to another.

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Neutrons

In 1932, James Chadwick discovered another sub-atomic particle within the nucleus. This particle had:

• No electrical charge (it was neutral).
• A mass nearly equal to that of a proton (approximately 1 u).

This particle was named the neutron (n).

Neutrons are present in the nucleus of all atoms, except for the simplest isotope of hydrogen (Protium).

Protons and neutrons together reside in the nucleus and are collectively called nucleons.

The mass of an atom is effectively the sum of the masses of the protons and neutrons in its nucleus, as the mass of electrons is negligible.

For example, a carbon atom with 6 protons and 6 neutrons has a mass of approximately 6 u (from protons) + 6 u (from neutrons) = 12 u. An aluminium atom with 13 protons and 14 neutrons has a mass of approximately 13 u + 14 u = 27 u.

How Are Electrons Distributed In Different Orbits (Shells)?

The arrangement of electrons in the various energy levels or shells around the nucleus is described by the Bohr-Bury scheme. This scheme follows certain rules for distributing electrons:

1. The maximum number of electrons that a shell can hold is given by the formula $2n^2$, where 'n' is the number of the orbit or energy level (n=1 for K shell, n=2 for L shell, n=3 for M shell, etc.).
   • K-shell (n=1): Maximum electrons = $2 \times 1^2 = 2$
   • L-shell (n=2): Maximum electrons = $2 \times 2^2 = 8$
   • M-shell (n=3): Maximum electrons = $2 \times 3^2 = 18$
   • N-shell (n=4): Maximum electrons = $2 \times 4^2 = 32$, and so on.
2. The outermost shell of an atom cannot accommodate more than 8 electrons, regardless of the $2n^2$ rule for inner shells.
3. Electrons fill the shells in a step-wise manner, starting from the innermost shell (K shell). A new shell is filled only after the inner shells are completely filled.

Following these rules, we can determine the electron distribution (electronic configuration) for atoms of different elements. For a neutral atom, the number of electrons is equal to the number of protons (atomic number).

Valency

The electrons located in the outermost shell of an atom are called valence electrons.

Atoms of elements with a completely filled outermost shell are chemically unreactive or inert (e.g., Noble gases like Helium with 2 electrons in K shell, and Neon or Argon with 8 electrons in their outermost shells). Their combining capacity is considered zero.

The tendency of atoms to react and form chemical bonds is driven by the desire to achieve a stable electron configuration in their outermost shell, similar to that of noble gases. For most atoms (except hydrogen and helium), this stable configuration is having eight electrons in the outermost shell, known as the octet rule.

Atoms achieve this octet by gaining, losing, or sharing valence electrons with other atoms.

The valency of an element is defined as the combining capacity of its atom. It is determined by the number of electrons an atom needs to gain, lose, or share to attain a stable outermost shell configuration (usually an octet).

Examples:

• Hydrogen, Lithium, and Sodium atoms have 1 electron in their outermost shell. They tend to lose this one electron to achieve stability (a duplet for H, and an octet for Li and Na in the inner shell). Their valency is 1.
• Magnesium has 2 valence electrons; it tends to lose 2. Its valency is 2.
• Aluminium has 3 valence electrons; it tends to lose 3. Its valency is 3.
• Fluorine has 7 valence electrons. It is easier to gain 1 electron to complete its octet (8-7=1). Its valency is 1.
• Oxygen has 6 valence electrons. It is easier to gain 2 electrons to complete its octet (8-6=2). Its valency is 2.

Valency represents the number of electrons involved in forming bonds and determines how atoms combine to form compounds.

Atomic Number And Mass Number

The identity and properties of an element are fundamentally determined by the number of protons in its atoms.

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Atomic Number

The atomic number (Z) of an element is defined as the total number of protons present in the nucleus of an atom of that element.

Every atom of a particular element has the exact same atomic number. The atomic number is unique to each element and serves as its defining characteristic. For example, any atom with 1 proton is Hydrogen (Z=1), any atom with 6 protons is Carbon (Z=6).

For a neutral atom, the number of electrons orbiting the nucleus is equal to the number of protons in the nucleus (Number of electrons = Z).

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Mass Number

The mass of an atom is primarily concentrated in its nucleus due to the presence of protons and neutrons, which have significantly greater mass than electrons. As discussed, protons and neutrons are called nucleons.

The mass number (A) of an atom is defined as the sum of the total number of protons and neutrons present in its nucleus.

$ \text{Mass Number (A)} = \text{Number of Protons (Z)} + \text{Number of Neutrons} $

To represent an atom, the atomic number, mass number, and symbol of the element are often written together in the following format:

$$ \textsf{}_{\text{Z}}^{\text{A}}\text{X} $$

Where X is the symbol of the element, A is the mass number, and Z is the atomic number.

For example, Nitrogen (N) has 7 protons and typically 7 neutrons. Its atomic number Z=7 and mass number A = 7+7=14. It is represented as $\text{}_{\text{7}}^{\text{14}}\text{N}$.

Isotopes

Experiments revealed that atoms of the same element can sometimes have slightly different masses. This led to the discovery of isotopes.

Definition: Isotopes are atoms of the same element that have the same atomic number (Z) but different mass numbers (A). This difference in mass number arises because isotopes of an element have the same number of protons but a different number of neutrons.

Examples:

• Hydrogen (Z=1): Has three isotopes:
  • Protium ($\text{}_{\text{1}}^{\text{1}}\text{H}$): 1 proton, 0 neutrons, Mass Number = 1
  • Deuterium ($\text{}_{\text{1}}^{\text{2}}\text{H}$ or D): 1 proton, 1 neutron, Mass Number = 2
  • Tritium ($\text{}_{\text{1}}^{\text{3}}\text{H}$ or T): 1 proton, 2 neutrons, Mass Number = 3
• Carbon (Z=6): Common isotopes are $\text{}_{\text{6}}^{\text{12}}\text{C}$ (6 protons, 6 neutrons) and $\text{}_{\text{6}}^{\text{14}}\text{C}$ (6 protons, 8 neutrons).
• Chlorine (Z=17): Common isotopes are $\text{}_{\text{17}}^{\text{35}}\text{Cl}$ (17 protons, 18 neutrons) and $\text{}_{\text{17}}^{\text{37}}\text{Cl}$ (17 protons, 20 neutrons).

Many elements in nature exist as a mixture of two or more isotopes. Each individual isotope is considered a pure substance.

Properties of Isotopes:

• Chemical Properties: Isotopes of an element have the same number of protons and electrons (in a neutral atom), meaning they have the same electronic configuration. Since chemical properties are determined by electronic configuration (specifically valence electrons), isotopes generally exhibit very similar chemical properties.
• Physical Properties: Isotopes have different masses due to the varying number of neutrons. Physical properties like density, melting point, boiling point, and diffusion rate can be different for different isotopes of the same element.

Since elements exist as isotopic mixtures, the atomic mass listed for an element on the periodic table is usually an average atomic mass. This average is calculated based on the masses of its naturally occurring isotopes and their relative abundances (percentages).

Example: Calculating Average Atomic Mass of Chlorine:

Natural chlorine exists as $\text{}_{\text{17}}^{\text{35}}\text{Cl}$ with a mass of 35 u (approx.) and $\text{}_{\text{17}}^{\text{37}}\text{Cl}$ with a mass of 37 u (approx.). Their relative abundance in nature is approximately 3:1, meaning 75% is $^{35}\text{Cl}$ and 25% is $^{37}\text{Cl}$.

Average Atomic Mass of Cl = $( \text{Mass of } ^{35}\text{Cl} \times \text{Percentage Abundance} ) + ( \text{Mass of } ^{37}\text{Cl} \times \text{Percentage Abundance} )$

Average Atomic Mass of Cl = $ (35 \text{ u} \times \frac{75}{100}) + (37 \text{ u} \times \frac{25}{100}) $

Average Atomic Mass of Cl = $ (35 \times 0.75) \text{ u} + (37 \times 0.25) \text{ u} $

Average Atomic Mass of Cl = $ 26.25 \text{ u} + 9.25 \text{ u} = 35.5 \text{ u} $

The average atomic mass of chlorine is 35.5 u. This means a sample of natural chlorine will have this average mass per atom, even though no single chlorine atom actually has a mass of 35.5 u.

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Applications

While isotopes of an element behave similarly chemically, some isotopes have specific physical or nuclear properties that make them useful in various fields:

• An isotope of Uranium (Uranium-235) is used as a fuel in nuclear reactors for power generation.
• An isotope of Cobalt (Cobalt-60) is used in the treatment of cancer (radiotherapy).
• An isotope of Iodine (Iodine-131) is used in the treatment of goitre (a condition affecting the thyroid gland).

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Isobars

In contrast to isotopes, which are atoms of the same element, isobars are atoms of different elements that have the same mass number (A) but different atomic numbers (Z).

Since isobars are atoms of different elements, they have different numbers of protons and electrons, and therefore different chemical properties.

Example:

• Calcium ($\text{}_{\text{20}}^{\text{40}}\text{Ca}$): Atomic number Z=20 (20 protons), Mass number A=40. Number of neutrons = 40 - 20 = 20.
• Argon ($\text{}_{\text{18}}^{\text{40}}\text{Ar}$): Atomic number Z=18 (18 protons), Mass number A=40. Number of neutrons = 40 - 18 = 22.

Calcium and Argon are isobars because they have the same mass number (A=40) but different atomic numbers (Z=20 and Z=18).

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