Structure of Atom Formula: Principles, Models & Examples

The structure of atom formula depends upon the mass of protons, electrons and neutrons. Atoms are the fundamental building blocks of matter. They can join together to form molecules, which are the basic building blocks of life. 

• Atoms are the smallest units of an element. 
• The nucleus of an atom is extremely small and positively charged.
• The electrons are negatively charged. 
• Nuclei are usually less than a ten-thousandth as big as an atom but contain more than 99.9% of its mass. 
• Structure of atom formula helps in calculating the radius of the nucleus.
• It helps in determining the stability of atoms after the discovery of sub-atomic particles.
• Different elements (such as oxygen, carbon, and uranium) are made up of different types of atoms. 
• Atoms are also found in our daily lives.
• Carbon is made of organic matter and cells.

Key Terms: Structure of atom, Nucleus, Atomic Structure, Molecules, Electrons, Alpha particles, Proton, Neutron, Electron, Radioactivity, Orbit, Atomic Mass, Atomic Number, Electron Shell, Element

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Structure of Atom

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In atoms, a nucleus (centre) in which protons (positively charged) and neutrons (neutral) reside is called the atomic structure. Electrons, negatively charged particles, revolve around the nucleus' center. 

• The proton, electron and nucleus are components of an atom.
• Atomic number refers to the total number of protons found in the nucleus.
• Structure of atom is also known as atomic structure.
• Democritus was the first person to introduce the concept of the atom.
• One atomic mass unit (amu) or one Dalton is the unit of structure of atom formula.
• Scientists such as John Dalton, JJ Thomson, Ernest Rutherford and Niels Bohr made the greatest contributions to the field. 
• The discovery of particles inside atoms, results in development of chemical species, which are called subatomic particles. 

Structure of Atom

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Dalton’s Atomic Theory

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Dalton's atomic theory asserted that all atoms of an element were the same, but that atoms of different elements differed in size and mass

• In chemical reactions, atoms are rearranged to form products.
• He proposed that the atomic structure consisted of atoms that cause chemical reactions to take place. 
• Atoms are indivisible molecules. 
• Each element has a specific type of atom in it. 
• Each atom has its own constant mass, which varies from element to element. 
• As a result of a chemical reaction, atoms undergo rearrangement. 
• Atoms cannot be created nor destroyed but can be transformed from one form to another. 
• Several laws of chemical reactions have been successfully explained by Dalton's atomic theory, including the 
• The Law of Conservation of Mass and the Law of Constant Proportions was explained by Dalton's atomic theory.
• It also explains the Law of Multiple Proportions and the Law of Reciprocal Proportions.

Limitations of Dalton's Theory

Some major limitations of Dalton's theory are as follows:

• Isotopes could not be explained in this theory. 
• The theory does not explain the structure of an atom and its components.
• Scientists discovered particles inside the atom that helped prove the existence of divisible particles. 

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Thomson Model of Atom

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According to JJ Thomson's model, electrons were embedded into atoms in a manner which would give them the most stable electrostatic arrangement. Atoms were assumed to have spheres of positive electricity (positive charge) with a radius of 10 cm. 

• The model depicts the atom as a pudding or cake with raisins (electrons) embedded within it.
• It is also referred to as the 'raising pudding' model.
• Thomson discovered electrons by conducting a cathode ray experiment.
• The model describes the internal structure of the atom.
• It was, however, discarded by the Rutherford Atomic Model.

Limitations of the Thomson Model of Atom

This model of atoms did not explain Rutherford's gold foil experiment because it failed to account for the electrical neutrality of atoms. 

• The model fails to explain the stability of an atom.
• Thomson was not able to explain the position of the nucleus embedded in an atom.
• It fails to explain the scattering of alpha particles.

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Rutherford's Alpha Scattering Experiment

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In the Rutherford Scattering Experiment, the thin gold foil, which had a circular fluorescent ZnS screen surrounding it, was used. When ⍺-particles hit the screen, a tiny flash of light was produced. 

• Rutherford bombarded high-energy ⍺-particles from radioactive sources on thin gold foil (thickness 10^–7m).
• Since most of the a-particles pass through the foil, most of the space in an atom is empty. 
• In atoms, the positive charge must be concentrated in a region that repels and deflects a few positively charged particles. 
• The small area in the atom is called the nucleus. 
• Nucleus volume is very small in comparison with total atom volume. 
• The radius of the nucleus (10^–13 cm) is about 1/100,000 of the radius of the atom (10^–8 cm). 
• Atom's nucleus volume would be very small compared to its total volume. 
• Protons and neutrons, known as nucleons, make up the nucleus of an atom. 
• Nucleons are much heavier than electrons, suggesting that the mass of an atom resides in its nucleus. 
• Nuclear mass is the total number of nucleons. 
• Electrons are external to the nucleus and orbit the nucleus at high speed in a fixed circular path.

Rutherford ⍺-particles

Limitations of Rutherford Model

In order to revolve around the nucleus, electrons will need to spend energy, even though the nucleus exerts a strong attraction to them. Eventually, the electrons will lose all their energy and fall into the nucleus, so atom stability cannot be explained. 

• The type of spectrum expected if electrons continuously revolve around the nucleus would be a continuous spectrum.
• However, we see a line spectrum in reality.
• In these types of model, electron will collapse in the nucleus.
• Electrons would be disintegrated in 10^-8 seconds.

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Principles of Structure of Atom

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Some key principles of the structure of atoms are:

Aufbau’s Principle

Aufbau principle states that "atomic orbitals fill up in increasing energy levels". In other words, electrons occupy the lowest orbitals during the ground state.

• Electrons occupy orbitals with the lowest energy first. 
• This implies that electrons only enter orbitals with higher energies after the orbitals with lower energies have been filled entirely.
• (n+l) rule determines the order in which orbital energies increase.
• The sum of the azimuthal and principal quantum numbers is used to determine orbital energy levels. 
• Orbitals with values equal to (n+l) indicates the lower n value has lower energy associated with it.
• The order in which electrons fill the orbitals is: 1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, 5s, 4d, 5p, 6s, 4f, 5d, 6p, 6s, 4f, 5d, 6p, 7s, 5f, 6d, 7p, etc. 

Aufbau Principle

Pauli’s Exclusion Principle

According to the Pauli exclusion principle, no two electrons in the same atom will possess the same quantum numbers (n, l, ml, and ms). A single electron should have its own unique (singlet state) due to this Principle. 

There are two salient rules that follow: 

• Only two electrons can occupy the same orbital. 
• They need to have opposite spins or be antiparallel if they are in the same orbital.

In addition to electrons, Pauli's Exclusion Principle also applies to fermions and other particles with half-integer spins. Integer spin particles such as bosons, which have symmetric wave functions, are not affected by it. 

• Additionally, bosons are capable of sharing or possessing the same quantum states.
• Fermions are named after the Fermi-Dirac statistical distribution.

Pauli’s Exclusion Principle

Hund’s Rule of Maximum Multiplicity

An atom or molecule with one or more open electronic shells is predicted by Hund's rule of maximum multiplicity. It is based on the observation of atomic spectra. The lowest energy electron configuration has the greatest spin multiplicity.

• This means that electrons occupy two or more orbitals of equal energy singly before filling them in pairs.
• It is applicable when two or more orbitals of equal energy are available. 
• All electrons will have same spin to maximize overall spin.

Hund’s Rule of Maximum Multiplicity

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Formulas of Atomic Structure

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Some important formulas of atomic structure are as follows:

• Estimating the closest distance for the approach of alpha-particles:

 \(R = \frac{4KZe^2}{m_aV_a^2}\)

• Finding out the radius of nucleus

R = R₀ (A)^1/3 cm

• Heisenberg’s Uncertainty Principle

Δx . Δp >\(\frac{h}{4 \pi}\) or m Δx . Δv ≥ \(\frac{h}{4 \pi}\) or Δx . Δv ≥ \(\frac{h}{4\pi m}\)

• Planck’s Quantum Theory: Energy of one photon

hv = \(\frac{hc}{\lambda}\)

• Bohr’s Model for Hydrogen and Hydrogen-like atoms:

mvr = n \(\frac{h}{2 \pi}\) (Quantization of angular momentum)

E_n = – \(\frac{E_1}{n^2} z^2\)= 2.178 x 10^-18 \(\frac{z^2}{n^2}\) J / atom = 13.6 \(\frac{z^2}{n^2}\) eV; E₁ = \(\frac{-2 \pi^2me^4}{n^2}\)

r_n = \(\frac{n^2}{z}\) x \(\frac{n^2}{4 \pi^2 e^2 m} = \frac{0.529 * n^2}{z} A\)

v = \(\frac{2\pi ze^2}{nh} = \frac{2.18 * 10^6 * z}{n} m/s\)

• Photoelectric Effect

hv = hv₀ + \(\frac{1}{2}m_e v^2\)

• Number of photons which are emitted by a Hydrogen atom sample

 \(\frac{\Delta n (\Delta n + 1)}{2}\)

• De Broglie’s Wavelength

 \(\lambda = \frac{h}{mc} = \frac{h}{p}\) (for photon)

• Wavelength of the emitted photon

​\(\frac{1}{\lambda} = \bar{v} = RZ^2 (\frac{1}{n_1^2} - \frac{1}{n_2^2})\)

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Quantum Number Formulas

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The important Quantum Number formulas are as follows:

• Principle quantum number (n) = 1, 2, 3, 4 ….. to ∞.
• Orbital angular momentum of electron in any orbit = \(\frac{nh}{2 \pi}\)
• Azimuthal quantum number (l) = 0, 1, ……. to (n – 1)
• Number of orbitals in a subshell = 2l + 1
• Maximum number of electrins in particular subshell = 2 x (2l + 1)
• Orbital angular momentum:

L = \(\frac{h}{2 \pi} \sqrt{l (l +1)} = h \sqrt{l (l +1)}\)

[\(h = \frac{h}{2 \pi}\)]

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Things to Remember

• Structure of atom formula helps in determining the radius of nucleus.
• When a discharge passes through hydrogen gas under low pressure, hydrogen atoms are formed, which emit visible light. 
• The four lines that are visible to the eye can be observed with a Spectroscope or Spectrometer.
• Quantised energies and angular momenta can be used to specify atomic orbitals.

• Structure Of Atoms: Important Questions and Structure of Atom Class 11 MCQ will help you improve your understanding about the concept.

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Previous Year Questions

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• Band spectrum is also called…
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• The nuclei of which one of the following pairs of nuclei are isotones… ?
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