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In 1912, Niels Bohr proposed an atomic model in which electrons move around the nucleus, just as the planets in the solar system move around the sun. But the difference between the two is that Bohr proposed that electrons can only occupy certain energy levels proportional to the Planck constant, which he calls atomic orbitals. In other words, the energy of electrons in these orbitals is quantized. When electrons move from a higher orbit to a lower orbit, they release energy in the form of photons; when they move from a lower orbit to a higher orbit, they absorb energy. Bohr's original equation is shown below, which points out that the energy depends on the quantum number n, which is the orbit of the electron.

This model solves several problems in classical physics and contributes to our current understanding of quantum mechanics. However, it can not accurately reproduce the experimental results of the light emitted by the atom, it only predicts the structure of the atom according to the main orbit and does not take into account the spin or relativistic effect of electrons. In other words, the atom has a finer structure, which has suborbitals.

According to Schrodinger, according to quantum mechanics, electrons are not confined to orbits like planets, but are waves of matter that form a probability cloud around the nucleus in 3D space. The Schrodinger equation describes the rules of this behavior and goes beyond Bohr's atomic model to more accurately describe the structure of every atom that exists in nature.

The Schrodinger equation shows that each electron shell has the maximum number of electrons it can hold. The innermost layer holds up to 2 electrons, the second layer holds up to 8 electrons, followed by 18, 32, 50, and so on. So what needs to be explained now is why these numbers are so special. Why does the interaction between atoms follow these numbers? It all comes down to energy.

Systems in the universe always tend to their lowest energy state. In order to minimize energy, electrons always fill from the inner layer and move outward. It can be proved that whether the shell is full or empty minimizes the energy of the atom. In order to understand the reason, we must solve the Schrodinger equation. Although this equation looks scary, it is essentially an expression of conservation of energy. Simply put, the total energy is equal to the kinetic energy plus the potential energy.

It is easiest to solve this equation by using hydrogen atoms because it is the simplest atom with only one electron revolving around a proton. Because the nucleus is made up of a proton, it is spherically symmetric. This spherical symmetry can make the solution simple enough, which is very important for solving the Schrodinger equation accurately. Although we use the simplest model, it takes a lot of time and paper to deduce in order to obtain the wave function of hydrogen atom.

In this wave function, we mainly focus on three parameters: n, l and m. N represents the electron shell, and naphth1 is the ground state, which is the lowest energy state of hydrogen. But hydrogen is not always in the lowest energy state, so it can have other values. L is the quantum number of the shell angular momentum. M is the number that specifies the direction of the shell space. When we insert different values of nlm into the equation, it also approximately represents the solution of all the electronic quantum states of any other atom. So this equation allows us to predict the electronic behavior of all the elements in the periodic table.

Now, we are going to explain the range of these three numbers. First, they must all be integers. Because n represents the electron shell, it must be valued from 1, while l is an integer from 0 to nmur1, and m is an integer from-l to + l. For example, if naughty 1, then lumb0 and mord0 are not naughty 2, then lumb0 or 1 may be masked 1, 0 or 1.

Thus, there are 1 possible configurations when nforth 1, 4 possible configurations when nasty 2, 9 possible configurations when nforth 3, and so on. Don't forget that the electron is a fermion, and its spin is 1x2, and its direction can be up or down, so we have to multiply these configurations by 2, that is, 2, 8, 18, 32.

Just solving the Schrodinger equation of the hydrogen atom allows us to apply it to all the elements of the periodic table. However, this is not entirely accurate, there will be some small changes for larger atoms, and the shell may be occupied in a slightly different way.

This article comes from the official account of Wechat: Vientiane experience (ID:UR4351), author: Eugene Wang

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