I am having some chemistry problems.
3. The graph compares the 1s orbital energies for the F atom (Z = 9), the Ne+ ion (Z = 10), and the Na++ ion (Z = 11).
(the graph shows F having an Orbital Energy of 692.45, Ne+ with 47.74, and Na++ with 33.52)
a. How many electrons does each species have?
b. According to the graph, which species is most stable?
c. Use Coulomb's law to explain the energy measurements shown in the graph and how this affects the distribution of electrons.
a. Well, let's do some electron counting, shall we? So, the F atom has an atomic number Z = 9, meaning it has 9 electrons. The Ne+ ion has Z = 10, which means it's lost one electron compared to the neutral Ne atom, so it has 10 - 1 = 9 electrons. Finally, the Na++ ion has Z = 11, which means it has lost two electrons compared to the neutral Na atom, so it has 11 - 2 = 9 electrons as well.
b. Ah, the stability question. According to the graph, the species with the lowest orbital energy is the Na++ ion (Z = 11) with an energy of 33.52. So, I guess we could say it's the most stable of the three.
c. Now, let's take a dive into Coulomb's law: F = k * |q1 * q2| / r^2. This equation relates the force (F) between two electric charges (q1 and q2) with the distance between them (r) and the constant of proportionality (k). In our case, the charges are the electron and the nucleus.
The energy measurements shown in the graph reflect the potential energy of the electrons in relation to the nucleus. As the atomic number (Z) increases, the positive charge of the nucleus also increases. So, the attraction between the electrons and the nucleus becomes stronger.
This increase in attraction results in a decrease in the energy of the electrons, causing them to be closer to the nucleus. Since the energy of the electrons is related to their distance from the nucleus, the closer they are, the lower their energy will be.
So, the energy measurements on the graph show how the increase in nuclear charge due to a higher atomic number affects the distribution of electrons by pulling them closer to the nucleus and lowering their energy levels.
To answer these questions, we need to understand the electron configuration and the basic principles of Coulomb's law.
a. To determine the number of electrons for each species, we look at their atomic numbers (Z).
- The F atom (Z = 9) has 9 electrons.
- The Ne+ ion (Z = 10) indicates that it has lost one electron, so it has 10 - 1 = 9 electrons.
- The Na++ ion (Z = 11) has lost two electrons, so it has 11 - 2 = 9 electrons.
Therefore, all three species have 9 electrons each.
b. The graph shows the comparison of the 1s orbital energies. The lower the energy, the more stable the species is. According to the graph, F has the highest energy (692.45), Ne+ has a lower energy (47.74), and Na++ has the lowest energy (33.52). Therefore, Na++ is the most stable species.
c. Coulomb's law describes the electrostatic interaction between charged particles. In this case, it explains the energy measurements shown in the graph and the distribution of electrons.
The energy of an electron in an atom is influenced by two factors: the nuclear charge (Z) and the distance between the electron and the nucleus. According to Coulomb's law, the attractive force between the negatively charged electron and the positively charged nucleus increases as the nuclear charge increases. This leads to higher energy for the 1s orbital as the nuclear charge increases.
In the case of F, it has the lowest nuclear charge (Z = 9), resulting in the highest energy. Ne+ has lost one electron compared to its neutral state, resulting in a slightly lower energy. Na++ has lost two electrons compared to its neutral state, resulting in the lowest energy.
The distribution of electrons depends on the energy levels and sublevels available. In this case, all three species have 9 electrons, but the higher nuclear charge in Na++ causes the energy of the 1s orbital to decrease, making it more stable. This stable energy level allows for the efficient filling of higher energy orbitals with additional electrons.
In summary, the energy measurements shown in the graph are determined by Coulomb's law, where the nuclear charge affects the energy of the 1s orbital. The stability and distribution of electrons in each species depend on their respective energy levels and sublevels.