**The oxidation state of an element tells us about the:**

The oxidation state of an element is a measure of the degree of oxidation (loss of electrons) of an atom in a chemical compound. It is an important concept in chemistry as it helps us understand the electron distribution and the nature of chemical bonds in a compound. The oxidation state can provide valuable information about the reactivity and behavior of an element in a chemical reaction.

**Explanation:**

The correct answer to the given question is option 'E', which states that the oxidation state of an element tells us about all of the following:

a) Number of electrons gained
b) Number of electrons lost
c) Number of electrons shared
d) Degree of oxidation

Let's discuss each of these points in detail:

**a) Number of electrons gained:**

In a chemical reaction, an element can gain electrons, resulting in a negative oxidation state. When an atom gains electrons, its oxidation state decreases. For example, in the reaction between sodium (Na) and chlorine (Cl) to form sodium chloride (NaCl), sodium loses an electron and chlorine gains an electron. The oxidation state of sodium changes from 0 to +1, indicating the loss of one electron, while the oxidation state of chlorine changes from 0 to -1, indicating the gain of one electron.

**b) Number of electrons lost:**

Similarly, in a chemical reaction, an element can lose electrons, resulting in a positive oxidation state. When an atom loses electrons, its oxidation state increases. For example, in the reaction between magnesium (Mg) and oxygen (O2) to form magnesium oxide (MgO), magnesium loses two electrons and oxygen gains two electrons. The oxidation state of magnesium changes from 0 to +2, indicating the loss of two electrons, while the oxidation state of oxygen changes from 0 to -2, indicating the gain of two electrons.

**c) Number of electrons shared:**

In some chemical compounds, electrons are shared between atoms, resulting in a partial transfer of electron density. This sharing of electrons is seen in covalent bonds. The oxidation state can provide information about the number of electrons shared between atoms. For example, in the compound water (H2O), oxygen shares two electrons with two hydrogen atoms, resulting in an oxidation state of -2 for oxygen and +1 for each hydrogen atom.

**d) Degree of oxidation:**

The oxidation state also gives us information about the degree of oxidation of an atom in a compound. It indicates the number of electrons an atom has lost or gained compared to its neutral state. A positive oxidation state indicates that an atom has lost electrons, while a negative oxidation state indicates that an atom has gained electrons. The magnitude of the oxidation state provides insights into the reactivity and behavior of an element in a chemical reaction.

In conclusion, the oxidation state of an element tells us about the number of electrons gained, number of electrons lost, number of electrons shared, and the degree of oxidation. It is a fundamental concept in chemistry that helps us understand the electron distribution and chemical behavior of elements in compounds.