Explain why we construct a Bohr model of the atom by first filling a lower shell to capacity before going to an upper shell.

The Bohr model of the atom, proposed by Niels Bohr, is a simplified representation of the structure of an atom. In this model, electrons orbit the nucleus (made up of protons and neutrons) in specific energy levels or shells. Each shell can hold a certain number of electrons, and as we move away from the nucleus, the shells can accommodate more electrons and have higher energy levels.

Each shell in the Bohr model has a specific capacity to hold electrons, based on the formula \(2n^2\), where 'n' is the shell number (counting from the nucleus outward). For example, the first shell (n=1) can hold up to 2 electrons, the second shell (n=2) can hold up to 8 electrons, the third shell (n=3) can hold up to 18 electrons, and so on.

Electrons in an atom tend to achieve the lowest possible energy state. This is because a lower energy state is more stable than a higher energy state. The more stable an electron is in its energy level, the less likely it is to be removed or to react with other atoms. The stability of an electron in an atom is achieved by filling the shells in order of increasing energy levels.

When constructing a Bohr model of an atom, we fill the lower shells to capacity before going to an upper shell. This is because electrons in lower energy levels are more stable and have lower energy than those in higher energy levels. By filling the lower shells first, we ensure that electrons achieve the most stable configuration possible within the atom.

Let's take a look at an example to better understand the concept. Carbon has 6 electrons. According to the Bohr model, these electrons will be distributed in the shells as follows: 1. The first shell (n=1, capacity=2) will be filled with 2 electrons. 2. The second shell (n=2, capacity=8) will be filled with the remaining 4 electrons. So, the electron configuration of a carbon atom will be: 1st shell - 2 electrons, 2nd shell - 4 electrons. This configuration ensures that the electrons in the carbon atom are in their lowest possible energy state, making the atom stable. In conclusion, we construct a Bohr model of the atom by first filling a lower shell to capacity before going to an upper shell because it allows electrons to achieve the lowest possible energy state, making the atom more stable.