Problem 68 - Chemistry The Central Science In Si Units

Question

(a) The average distance from the nucleus of a 3 s electron in a chlorine atom is smaller than that for a \(3 p\) electron. In light of this fact, which orbital is higher in energy? (b) Would you expect it to require more or less energy to remove a \(3 s\) electron from the chlorine atom, as compared with a \(2 p\) electron?

Step-by-Step Solution

Answer

(a) The 3p orbital is higher in energy. (b) It requires less energy to remove a 3s electron than a 2p electron.

Step 1: Analyze Orbital Sizes

The average distance from the nucleus is relevant to the energy of electrons. The 3s electron orbits closer to the nucleus on average than a 3p electron. Electrons closer to the nucleus experience a stronger attraction due to Coulomb's law.

Step 2: Relate Distance to Energy

Since 3s electrons are on average closer to the nucleus than 3p electrons, they are held more tightly and have lower energy due to stronger attraction to the nucleus. Hence, the 3p orbital is higher in energy than the 3s orbital.

Step 3: Consider Ionization Energy

Ionization energy is the energy required to remove an electron from an atom. Since 3s electrons are closer to the nucleus and more tightly bound, it requires more energy to remove a 3s electron than a 3p electron.

Step 4: Compare with 2p Electrons

The 2p electrons are even closer to the nucleus than 3s electrons and are more tightly bound. Consequently, more energy is required to remove a 2p electron than a 3s electron due to their higher core attraction.

Key Concepts

Electron Orbitals

In an atom, electrons are not just randomly scattered around the nucleus. Instead, they reside in specific regions called electron orbitals. These orbitals are described as clouds of possible locations where an electron can be found. They are influenced by quantum mechanics, which organizes them into different shapes and volumes. Electrons in the same energy level are usually organized into different types of orbitals like s, p, d, and f, each having a unique shape. The s orbital is spherical while the p orbitals are shaped like dumbbells. The volume or the area of these orbital clouds determines the average distance electrons remain from the nucleus. In terms of energy, the closer the orbital is to the nucleus, generally, the lower its energy level is because the electron is attracted by the nucleus more strongly.

Energy Levels

An atom's energy levels are like rungs on a ladder, where electrons can jump from one rung to another. These levels are organized based on the principal quantum number n, and signify the potential energy of the electrons. The farther the electron is from the nucleus, the more energy it possesses. Energy levels also determine the electromagnetic characteristics of the atom. Electrons tend to occupy the lowest energy levels available, which is a concept known as the Aufbau principle. Within the same principal energy level, different orbitals, such as s and p, can have different energies due to their shapes and distances from the nucleus. For instance, in chlorine, a 3s orbital's electrons are closer to the nucleus compared to those in a 3p orbital, thus, the 3s is lower in energy.

Ionization Energy

Ionization energy refers to the amount of energy required to remove an electron from an atom. It is a crucial concept in understanding atomic reactivity and chemical bonding. In general, electrons that are closer to the nucleus are more tightly bound and therefore need more energy to be removed. This principle explains why removing a 3s electron from a chlorine atom requires more energy than removing a 3p electron, as the 3s orbital is closer to the nucleus. By contrast, the energy required to remove electrons closer to the nucleus, such as 2p electrons, is even higher, demonstrating the increasing strength of the atomic attraction. Therefore, ionization energy usually increases across a period in the periodic table as electrons fill orbitals closer to the nucleus or as effective nuclear charge increases.