What Is The Quantum Mechanical Model Of The Atom And How Does It Explain Atomic Structure
The wave equation of Schrodinger's and its solutions serve as the foundation for the quantum mechanical model. The concept of shells, subshells, and orbitals is introduced by the wave equation solution. Newton's laws of motion, the foundation of conventional mechanics, can be used to explain the movement of entities that people encounter daily accurately.
According to classical mechanics, a particle's location and momentum determine its physical nature. If one is aware of both of these characteristics, one can use classic mechanics to forecast the system's prospective state in relation to the force operating on it. The dual nature of matter, which is important for microscopic particles, is ignored by classic mechanics. As a result, it cannot account for the mobility of small particles.
A novel mechanical model termed a quantum mechanical model of atom was established on the basis of the dual nature of microscopic particles and Heisenberg's principle. Thus this article provides more detailed knowledge of the quantum mechanical model of the atom and its important features.
What is the Quantum Mechanical Model of an Atom?
The model that underpins contemporary knowledge of the atom is regarded as the quantum mechanical model of atom. Schrodinger's wave equation cannot be precisely solved for a multi-electron atom, making its application to multi-electron atoms challenging. Approximate techniques were used to get around this problem. The Schrodinger wave equation was used to determine the structure of an atom, which resulted in the development of the quantum mechanical model of atom.
Schrodinger Wave Equation
The Schrodinger wave equation describes how the wave function of space changes based on the field of force that an electron is moving through. The time-independent Schrodinger equation is,
\[\hat H\Psi = E\Psi \]
Here H^ is known as the Hamiltonian operator.
The wave function, which is represented by the symbol Ψ, is a function of the particle's location coordinates Ψ(x, y, z) E is the system's energy.
\[\hat H = \left[ {\frac{{ - {h^2}}}{{8{\pi ^2}m}}\left( {\frac{{{\partial ^2}}}{{\partial {x^2}}} + \frac{{{\partial ^2}}}{{\partial {y^2}}} + \frac{{{\partial ^2}}}{{\partial {z^2}}}} \right) + V} \right]\]
The time-independent Schrodinger equation can also be written as,
\[\left[ {\frac{{ - {h^2}}}{{8{\pi ^2}m}}\left( {\frac{{{\partial ^2}\psi }}{{\partial {x^2}}} + \frac{{{\partial ^2}\psi }}{{\partial {y^2}}} + \frac{{{\partial ^2}\psi }}{{\partial {z^2}}}} \right) + V\psi } \right] = E\psi \]
Multiplying -8π2m/h2 and rearranging,
\[\frac{{{\partial ^2}\psi }}{{\partial {x^2}}} + \frac{{{\partial ^2}\psi }}{{\partial {y^2}}} + \frac{{{\partial ^2}\psi }}{{\partial {z^2}}} + \frac{{8{\pi ^2}m}}{{{h^2}}}\left( {E - V} \right)\psi + 0\]
The aforementioned Schrodinger wave equation is considered a Schrodinger wave equation of time independent since it excludes time as a variable. The particular values of E, the overall energy, allow for this equation's solution. i.e., the system's energy is quantised. The associated wave functions represent the atomic orbitals, which correspond to the permissible overall energy values known as Eigenvalues.
What are the Main Features of a Quantum Mechanical Model of an Atom?
The electrons in atoms possess quantified energy.
The wave-like characteristics of electrons directly contribute to the presence of quantified electronic energy levels. Schrodinger wave equation results provide the permitted levels of energy.
Heisenberg's uncertainty principle states that it is impossible to identify an electron's precise location and momentum using absolute accuracy. As a result, the orbital was first established by quantum mechanics. The probability of discovering an electron is higher in the three-dimensional space known as orbital.
The wave function Ψ, which depicts an atomic orbital, is obtained from the Schrodinger wave equation's result for the permitted energies of an atom. The wave function Ψ is an effective way to describe the wave behaviour of an electron in an orbital.
There is no physical significance to the wave function on its own. Nevertheless, the probability of detecting the electron in a tiny volume dxdydz surrounding a point (x, y, z) is x proportional to |Ψ(x, y, z) |2. This dxdydz |Ψ (x, y, z) |2 is called probability density and is constantly positive.
Interesting Facts
The area that an atom's electron will most probably be in for 90 per cent of the time is known as its atomic orbital.
The electron could only take highly precise circular orbits surrounding the nuclei in the Bohr model. A radical divergence from that is the quantum mechanical model.
The Schrodinger wave equation's solutions, known as wave functions, only provide the probability that an electron will be found at a specific location within the nucleus.
The term "electron cloud" is frequently used to describe where the electrons are located in the quantum mechanical model of an atom.
Key Features to Remember
Bohr's theories regarding the position of the electron were replaced with an uncertainty parameter in the Schrodinger wave equation.
The quantum mechanical model of the atom is recognised as the theoretical foundation for the current study of the atom.
The only thing that can be said about the electron's position is the probability that it is someplace in a particular region.
The probability of discovering an electron in a particular area of the atom is represented by the square of the wave function Ψ2.
FAQs on Quantum Mechanical Model Of The Atom In Chemistry
1. What is the quantum mechanical model of the atom?
The quantum mechanical model of the atom describes electrons as wave-like particles whose positions are given by probability distributions called orbitals rather than fixed circular paths. It is based on quantum mechanics and the Schrödinger wave equation.
- Electrons have both particle and wave nature (wave–particle duality).
- Their exact position cannot be known; only the probability of finding an electron is predicted.
- Electron energies are quantized, meaning they exist in specific energy levels.
- Orbitals (s, p, d, f) describe the region of highest probability of finding an electron.
2. Who developed the quantum mechanical model of the atom?
The quantum mechanical model was primarily developed by Erwin Schrödinger in 1926, with major contributions from other scientists.
- Louis de Broglie proposed the wave nature of electrons.
- Werner Heisenberg formulated the uncertainty principle.
- Erwin Schrödinger developed the wave equation to describe electron behavior.
- Max Born interpreted the wave function as a probability distribution.
3. What is Schrödinger’s wave equation in the quantum mechanical model?
The Schrödinger wave equation is a mathematical equation that describes how the quantum state of an electron changes in an atom. It is commonly written as Ĥψ = Eψ for stationary states.
- Ĥ is the Hamiltonian operator (total energy operator).
- ψ (psi) is the wave function of the electron.
- E is the quantized energy of the electron.
4. What are atomic orbitals in the quantum mechanical model?
An atomic orbital is a three-dimensional region around the nucleus where the probability of finding an electron is maximum. Orbitals arise as solutions of the Schrödinger equation.
- s-orbitals: spherical in shape.
- p-orbitals: dumbbell-shaped.
- d- and f-orbitals: more complex shapes.
- Each orbital can hold a maximum of 2 electrons with opposite spins.
5. What are the four quantum numbers and what do they represent?
The four quantum numbers describe the unique state of an electron in an atom: n, l, ml, and ms.
- Principal quantum number (n): energy level and size of the orbital (n = 1, 2, 3...).
- Azimuthal quantum number (l): subshell type (0 = s, 1 = p, 2 = d, 3 = f).
- Magnetic quantum number (ml): orientation of the orbital.
- Spin quantum number (ms): electron spin, +½ or −½.
6. What is the difference between Bohr’s model and the quantum mechanical model?
The main difference is that Bohr’s model places electrons in fixed circular orbits, while the quantum mechanical model describes electrons as probability clouds in orbitals.
- Bohr’s model works mainly for hydrogen-like atoms.
- The quantum model applies to multi-electron atoms.
- Bohr used classical physics with quantized energy levels.
- The quantum model uses wave functions and probability.
7. What is Heisenberg’s uncertainty principle?
The Heisenberg uncertainty principle states that it is impossible to simultaneously determine the exact position and momentum of an electron. It is mathematically expressed as Δx · Δp ≥ h/4π.
- Δx = uncertainty in position.
- Δp = uncertainty in momentum.
- h = Planck’s constant (6.626 × 10−34 J·s).
8. How are electron configurations written using the quantum mechanical model?
Electron configurations are written by filling atomic orbitals in order of increasing energy according to the Aufbau principle, Pauli exclusion principle, and Hund’s rule.
- Follow the order: 1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, etc.
- Each orbital holds a maximum of 2 electrons with opposite spins.
- Electrons occupy degenerate orbitals singly before pairing.
9. Why are electron energies quantized in the quantum mechanical model?
Electron energies are quantized because only specific wave functions satisfy Schrödinger’s equation for an atom.
- Electrons behave as standing waves around the nucleus.
- Only certain wavelengths fit allowed boundary conditions.
- Each allowed solution corresponds to a specific energy level.
10. What is the importance of the quantum mechanical model in chemistry?
The quantum mechanical model is important because it explains atomic structure, chemical bonding, and periodic trends accurately.
- Predicts electron configuration and valency.
- Explains spectral lines of elements.
- Forms the basis of chemical bonding theories like valence bond theory and molecular orbital theory.
- Helps understand reactivity, ionization energy, and atomic size.
