Features Of The Quantum Mechanical Model Of Atom

At the subatomic level, matter begins to act differently. Some of this conduct is so bizarre that we can only describe it through symbols and metaphors, as in poetry. What does it imply, for example, to state that an electron acts like a particle and a wave? Or that an electron doesn’t reside in a single spot, but rather is dispersed across the entire atom?

If these questions seem strange, it’s because they are! We are, as it turns out, in excellent company.

“Anyone who is not astonished by quantum theory has not comprehended it,” stated physicist Niels Bohr. If we’re having trouble understanding quantum physics, remember that the scientists who created it were just as perplexed.

Schrödinger equation

The Schrodinger wave equation is a mathematical statement that describes the energy and location of an electron in space and time while accounting for the electron’s matter wave nature within an atom.

It is founded on three factors. :

• The equation of a planar wave in its classical form,

• Broglie’s Matter-Wave Hypothesis, and

• Conservation of Energy.

The Schrodinger equation describes the shape of the wave functions or probability waves that influence the motion of some smaller particles in great detail. The equation also illustrates how external influences affect these waves. Furthermore, the equation employs the energy conservation idea, which provides information on the behaviour of an electron linked to the nucleus.Furthermore, we may determine the quantum numbers as well as the orientations and shapes of orbitals where electrons are present in a molecule or an atom by solving the Schrödinger equation.The time-dependent Schrödinger equation and the time-independent Schrödinger equation are the two equations.

The time-dependent Schrödinger equation looks like this:

iħd |¥(t)) = Ĥ|¥(t)).

Features Of The Quantum Mechanical Model

• An electron’s energy is quantized, which means that it can only have particular energy values.
• The permitted solution of the Schrödinger wave equation is the quantized energy of an electron, which is the outcome of the electron’s wave-like characteristics.
• The precise position and momentum of an electron cannot be known, according to Heisenberg’s Uncertainty Principle. So the sole chance of finding an electron at a given place can be calculated, and it is |ψ|² at that point, which represents the electron’s wave-function.
• The wave-function (ψ) of an electron in an atom is called an atomic orbital. An electron occupies an atomic orbital whenever it is characterised by a wave function. There are multiple atomic orbitals for an electron since it can have different wave functions. Every wave function or atomic orbital has a certain shape and energy. The orbital wave function of an atom stores all of the information about the electron in the atom, and quantum mechanics allows this information to be extracted.
• The likelihood of finding an electron at a certain site within an atom is equal to the square of the orbital wave function at that location, i.e. |ψ|². The probability density is always positive and is known as |ψ|².

Conclusion

Erwin Schrödinger (1887–1961), an Austrian scientist, exploited the electron’s wave-particle duality to formulate and solve a difficult mathematical equation that precisely explained the behaviour of the electron in a hydrogen atom in 1926. The answer to Schrödinger’s equation gave rise to the quantum mechanical model of the atom. In order to answer the equation, the electron energies must be quantized. In contrast to the Bohr model, quantization was simply assumed without any mathematical foundation. Remember that the electron’s exact journey in the Bohr model was limited to relatively well-defined circular orbits around the nucleus. The quantum mechanical paradigm, on the other hand, represents a complete departure from this. Wave functions, which are solutions to the Schrödinger wave equation, only indicate the chance of detecting an electron at a certain position surrounding the nucleus. Electrons do not move in simple circular orbits around the nucleus.