The Structure Of An Atom

The discovery of electrons and protons within the atom contradicted Dalton's idea of an indivisible atom. This prompted scientists to propose various models to explain the internal structure of the atom.

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Thomson’s Model Of An Atom

J.J. Thomson proposed one of the first models for the structure of an atom in 1898. His model is often compared to a Christmas pudding or a watermelon.

According to Thomson's model:

• An atom is considered to be a **sphere of uniformly distributed positive charge**.
• The **electrons are embedded** within this positively charged sphere, like currants in a Christmas pudding or seeds in a watermelon.

• The magnitude of the negative charges (from electrons) is **equal to the magnitude of the positive charge** in the sphere. This makes the atom as a whole electrically neutral.

Thomson's model successfully explained the overall neutrality of the atom. However, it could not explain the results of later experiments, particularly Rutherford's alpha-particle scattering experiment, which indicated that the positive charge was concentrated in a very small region, not spread uniformly.

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Rutherford’s Model Of An Atom

Ernest Rutherford, a student of J.J. Thomson, conducted experiments to investigate the arrangement of electrons within the atom. In 1911, he performed his famous **alpha-particle scattering experiment**.

In this experiment:

• A beam of fast-moving **alpha ($\alpha$) particles** (which are positively charged helium nuclei, ⁴₂He²⁺, with a mass of 4 u) was directed at a very **thin gold foil** (about 1000 atoms thick). Gold was chosen because it is highly malleable and could be made into an extremely thin sheet.
• A screen was placed around the gold foil to detect the deflected $\alpha$-particles.
• Based on Thomson's model (where positive charge is spread out), Rutherford expected the heavy, fast-moving $\alpha$-particles to pass straight through the thin gold foil with only minor deflections, as the positive charge would not be concentrated enough to cause large deviations.

However, the experimental results were surprisingly different:

• Most of the $\alpha$-particles ($\approx 99.9\%$) **passed straight through** the gold foil without any deflection.
• Some $\alpha$-particles were deflected by **small angles**.
• A very few $\alpha$-particles (about 1 in 12,000) were deflected back by nearly **180°** (appeared to rebound).

These unexpected results led Rutherford to draw the following conclusions about the structure of the atom:

• Since most $\alpha$-particles passed straight through, most of the space inside the atom must be **empty**.
• The deflection of some particles, especially the rare large-angle deflections and rebounds, indicated that the **positive charge** and most of the **mass** of the atom are concentrated in a very **small volume** at the centre. A direct collision between a positively charged $\alpha$-particle and this concentrated positive mass caused the large deflections and rebounds.
• This small, dense, positively charged region at the centre of the atom was named the **nucleus**.

Based on these conclusions, Rutherford proposed the **Nuclear Model of the Atom**:

• An atom has a tiny, positively charged **nucleus** at its centre, which contains nearly all the mass of the atom.
• The **electrons revolve** around the nucleus in well-defined circular paths (orbits).
• The size of the nucleus is extremely small compared to the overall size of the atom (the radius of the atom is about $10^5$ times larger than the radius of the nucleus).

Drawbacks of Rutherford’s Model:

Rutherford's model faced a major challenge regarding the stability of the atom. According to classical electromagnetic theory, a charged particle (like an electron) moving in a circular orbit around another charged particle (the nucleus) should continuously radiate energy. If the revolving electrons lost energy, they would spiral inwards and eventually crash into the nucleus. This would make the atom highly unstable and cause matter to collapse, which contradicts the observed stability of atoms.

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Bohr’s Model Of Atom

To address the instability issue in Rutherford's model, Neils Bohr refined the atomic model in 1913. He proposed the following postulates for his model:

• Only certain special orbits, known as **discrete orbits** or stationary states, are allowed for electrons inside the atom.
• While revolving in these discrete orbits, electrons **do not radiate energy**. Each discrete orbit is associated with a fixed energy level.

These orbits or shells are also called **energy levels** or **energy shells**. They are designated by the letters K, L, M, N, ... or by the principal quantum numbers, n = 1, 2, 3, 4, ... respectively, starting from the orbit closest to the nucleus (n=1 is the K shell, n=2 is the L shell, and so on).

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Neutrons

In 1932, James Chadwick discovered another sub-atomic particle that was also located in the nucleus. This particle was electrically neutral (had no charge) and had a mass very close to that of a proton. It was named the **neutron**, symbolized as 'n'.

Neutrons are present in the nucleus of all atoms, with the sole exception of hydrogen-1 (protium), which has only a proton in its nucleus. Along with protons, neutrons are collectively called **nucleons** because they reside in the nucleus.

The discovery of neutrons explained why the mass of an atom was often greater than the total mass of its protons alone. The mass of an atom is therefore the sum of the masses of the protons and neutrons in its nucleus. For example, a carbon atom with 6 protons and 6 neutrons has a mass of approximately $6 \text{ u} + 6 \text{ u} = 12 \text{ u}$. An aluminium atom with 13 protons and 14 neutrons has a mass of approximately $13 \text{ u} + 14 \text{ u} = 27 \text{ u}$.

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How Are Electrons Distributed In Different Orbits (Shells)?

The distribution of electrons into the discrete energy levels or shells around the nucleus was explained by Bohr and Bury. Specific rules govern how electrons fill these shells:

• The maximum number of electrons that can be accommodated in any given shell is given by the formula $\mathbf{2n^2}$, 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.).
• Based on this rule:
  • K shell (n=1) can hold a maximum of $2 \times 1^2 = 2 \times 1 = 2$ electrons.
  • L shell (n=2) can hold a maximum of $2 \times 2^2 = 2 \times 4 = 8$ electrons.
  • M shell (n=3) can hold a maximum of $2 \times 3^2 = 2 \times 9 = 18$ electrons.
  • N shell (n=4) can hold a maximum of $2 \times 4^2 = 2 \times 16 = 32$ electrons, and so on.
• The **outermost shell** of an atom can accommodate a maximum of **8 electrons** (the octet rule, important for chemical stability). This rule applies even if the $2n^2$ formula would allow more (e.g., for the M shell, the maximum is 18, but it behaves as the outermost shell with a capacity of 8 for elements up to atomic number 18).
• Shells are filled in a **step-wise manner**. Inner shells must be filled or nearly filled before electrons can occupy the outer shells. Electrons first occupy the lowest energy levels (shells) available.

These rules determine the **electronic configuration** of an atom, which describes how its electrons are distributed in the different energy shells. Electrons in the outermost shell are called **valence electrons**, and they are crucial in determining an element's chemical properties and combining capacity.

Figure 4.4 in the text shows schematic diagrams illustrating the electronic configuration of the first eighteen elements. Table 4.1 provides the composition (protons, neutrons, electrons) and electron distribution for these elements.

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Valency

The **valency** of an element is its combining capacity – its ability to form chemical bonds with other atoms. This combining capacity is determined by the number of **valence electrons**, which are the electrons present in the outermost shell of an atom.

Atoms tend to react and form chemical bonds to achieve a stable electron configuration in their outermost shell. The most stable configuration is typically an **octet** (8 electrons) in the outermost shell, or a **duplet** (2 electrons) for very light elements like Helium. Atoms achieve this stability by gaining, losing, or sharing valence electrons.

The number of electrons that an atom loses, gains, or shares to attain a stable outermost shell (usually an octet) represents its valency.

• Elements with a completely filled outermost shell (like noble gases - Neon, Argon with 8 valence electrons, or Helium with 2) are chemically inert, meaning they have a combining capacity or valency of **zero**.
• Elements with 1, 2, or 3 valence electrons (like Hydrogen, Lithium, Sodium, Magnesium, Aluminium) tend to **lose** these electrons to achieve a stable inner shell (which is now the outermost and filled). The number of electrons lost equals their valency. Thus, the valency of H, Li, Na is 1; Mg is 2; Al is 3.
• Elements with 5, 6, or 7 valence electrons (like Nitrogen, Oxygen, Fluorine, Chlorine) tend to **gain** electrons to complete their octet. Their valency is calculated by subtracting the number of valence electrons from 8.
  • Fluorine has 7 valence electrons. Valency = 8 - 7 = 1. Fluorine tends to gain 1 electron.
  • Oxygen has 6 valence electrons. Valency = 8 - 6 = 2. Oxygen tends to gain 2 electrons.
  • Nitrogen has 5 valence electrons. Valency = 8 - 5 = 3. Nitrogen tends to gain 3 electrons.
• Elements with 4 valence electrons (like Carbon, Silicon) tend to **share** electrons to achieve a stable configuration, and their valency is typically 4.

Thus, valency provides a quantitative measure of an element's tendency to combine with other elements. The valencies of the first eighteen elements are listed in Table 4.1.

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Atomic Number And Mass Number

Two key numbers are used to describe the composition of an atom: the atomic number and the mass number.

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Atomic Number

The **atomic number (Z)** of an element is equal to the **total number of protons** present in the nucleus of an atom of that element. The number of protons is unique to each element and defines its identity. For example, every atom with 6 protons is a carbon atom (Z=6), and every atom with 1 proton is a hydrogen atom (Z=1).

In a neutral atom, the number of electrons is equal to the number of protons, so the atomic number also indicates the number of electrons in a neutral atom.

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Mass Number

The **mass number (A)** of an atom is the **sum of the total number of protons and neutrons** (nucleons) present in its nucleus. Since protons and neutrons have significant mass compared to electrons, the mass number essentially represents the total number of particles contributing significantly to the atom's mass, which is concentrated in the nucleus.

Mass Number (A) = Number of protons (Z) + Number of neutrons (n)

An atom is typically represented using the following notation:

$$ \text{_Z^A X} $$

Where:

• $\text{X}$ is the symbol of the element.
• $\text{A}$ is the Mass Number (written as a superscript on the left).
• $\text{Z}$ is the Atomic Number (written as a subscript on the left).

For example, Nitrogen is represented as $^{14}_7\text{N}$. This means Nitrogen has an atomic number (Z) of 7 (7 protons) and a mass number (A) of 14 (7 protons + 7 neutrons). Sulfur is $^{32}_{16}\text{S}$, meaning Z=16 (16 protons) and A=32 (16 protons + 16 neutrons).

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Isotopes

In nature, some elements exist as atoms that have the same atomic number (meaning they belong to the same element) but different mass numbers. These are called **isotopes**.

Isotopes are atoms of the same element that have the same number of protons (same atomic number, Z) but different numbers of neutrons, resulting in different mass numbers (A).

Examples of isotopes:

• **Hydrogen:** Exists in three isotopic forms:
  • Protium ($^1_1\text{H}$): 1 proton, 0 neutrons, A=1
  • Deuterium ($^2_1\text{H}$ or D): 1 proton, 1 neutron, A=2
  • Tritium ($^3_1\text{H}$ or T): 1 proton, 2 neutrons, A=3
• **Carbon:** Common isotopes are $^{12}_6\text{C}$ (6 protons, 6 neutrons) and $^{14}_6\text{C}$ (6 protons, 8 neutrons).
• **Chlorine:** Common isotopes are $^{35}_{17}\text{Cl}$ (17 protons, 18 neutrons) and $^{37}_{17}\text{Cl}$ (17 protons, 20 neutrons).

Since isotopes of an element have the same number of electrons and the same electronic configuration, they exhibit very **similar chemical properties**. However, due to the difference in the number of neutrons and hence mass, their **physical properties** (like density, melting point, boiling point) can be slightly different.

Many elements found in nature are mixtures of different isotopes. The atomic mass of such an element is taken as the **average atomic mass**, which is a weighted average based on the relative abundance (percentage) of each isotope in nature.

For example, chlorine exists as $^{35}\text{Cl}$ with approximately 75% abundance and $^{37}\text{Cl}$ with approximately 25% abundance.

Average atomic mass of Chlorine = $\left( \text{Mass of }^{35}\text{Cl} \times \frac{\%\text{ Abundance of }^{35}\text{Cl}}{100} \right) + \left( \text{Mass of }^{37}\text{Cl} \times \frac{\%\text{ Abundance of }^{37}\text{Cl}}{100} \right)$

Average atomic mass of Chlorine = $\left( 35 \text{ u} \times \frac{75}{100} \right) + \left( 37 \text{ u} \times \frac{25}{100} \right)$

Average atomic mass of Chlorine = $\left( 35 \times \frac{3}{4} \right) + \left( 37 \times \frac{1}{4} \right) \text{ u}$

Average atomic mass of Chlorine = $\frac{105}{4} + \frac{37}{4} \text{ u} = \frac{142}{4} \text{ u} = 35.5 \text{ u}$

This calculated average atomic mass of 35.5 u is what is listed for chlorine. It's important to note that no single chlorine atom has a mass of 35.5 u; this is a statistical average over a large sample of chlorine atoms.

Applications of Isotopes:

While isotopes of an element behave chemically similarly, some isotopes have specific physical properties (like radioactivity) that make them useful in various applications:

• An isotope of **Uranium** ($^{235}\text{U}$) is used as fuel in nuclear reactors for generating electricity.
• An isotope of **Cobalt** ($^{60}\text{Co}$) is used in the treatment of cancer (radiotherapy).
• An isotope of **Iodine** ($^{131}\text{I}$) is used in the treatment of goitre (a thyroid condition) and as a tracer in medical imaging.
• The isotope $^{14}\text{C}$ is used in **carbon dating** to estimate the age of ancient organic materials.

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Isobars

Another term related to atomic composition is **isobars**.

Isobars are atoms of different elements that have different atomic numbers (Z) but the same mass number (A).

This means isobars have a different number of protons (since Z is different) and thus belong to different elements. However, the total number of nucleons (protons + neutrons) is the same in their nucleus.

Examples of isobars:

• **Calcium** ($^{40}_{20}\text{Ca}$): Z=20, A=40 (20 protons + 20 neutrons)
• **Argon** ($^{40}_{18}\text{Ar}$): Z=18, A=40 (18 protons + 22 neutrons)

Calcium and Argon are different elements (different Z) but have the same mass number (A=40). Isobars have different chemical properties because they are different elements with different numbers of electrons.

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H, D, and T represent the three isotopes of Hydrogen: Protium ($^1_1\text{H}$), Deuterium ($^2_1\text{H}$), and Tritium ($^3_1\text{H}$). The atomic number (Z) for all is 1, meaning they all have 1 proton and, in a neutral atom, 1 electron. The mass number (A) is Protons + Neutrons.

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