Question

One isotope of a metallic element has mass number 137 and 82 neutrons in the nucleus. The cation derived from the isotope has 54 electrons. Write the chemical symbol for this cation.

Short answer

The chemical symbol for the cation is \(\text{Cs}^+\).

Step-by-step solution

Determine the number of protons

The number of protons in an atom can be found by subtracting the number of neutrons from the mass number. The mass number is given as 137 and there are 82 neutrons. Thus, the number of protons is calculated as: \(137 - 82 = 55\).

Identify the element

The number of protons corresponds to the atomic number of the element. An atomic number of 55 corresponds to the element Cesium, which has the chemical symbol \(\text{Cs}\).

Determine the charge of the cation

We know the cation has 54 electrons. A neutral atom of Cesium has 55 electrons (since it has 55 protons to balance the charge). Losing one electron results in a cation with 54 electrons, indicating a \(+1\) charge.

Write the chemical symbol for the cation

The chemical symbol for the cation is written using the element symbol and the charge. Since we've identified the element as Cesium (Cs) and it has a \(+1\) charge, the chemical symbol for the cation is \(\text{Cs}^+\).

Key concepts

Atomic Number

The atomic number is a fundamental property of an element. It tells you the number of protons in the nucleus of an atom and determines which chemical element you are dealing with. Each element has a unique atomic number. For example, in the case of cesium, the atomic number is 55, meaning every cesium atom has 55 protons.

When identifying an element, looking at its atomic number is key. This number is crucial because it also reflects the number of electrons in a neutral atom, which balances the positive charge of the protons. Therefore, the entire identity of an element hinges on its atomic number.

Mass Number

The mass number is the total count of protons and neutrons in an atom's nucleus. It gives us an indication of the atom's mass since protons and neutrons account for most of an atom's weight.

To find the mass number, you simply add the number of protons and neutrons together. For instance, if you have an isotope of cesium with a mass number of 137 and it contains 82 neutrons, you can find the number of protons by subtracting 82 from 137, which gives you 55 protons.

Unlike the atomic number, different isotopes of the same element can have different mass numbers because they contain different numbers of neutrons. However, the number of protons, which is the atomic number, always remains the same for a given element.

Chemical Symbol

Chemical symbols are unique one- or two-letter abbreviations for elements derived from their English or Latin names. They provide a standardized way to represent elements. For cesium, the chemical symbol is Cs, derived from its name, and it is a quick reference for the single element cesium without writing its full name.

Understanding chemical symbols is critical in chemistry as they are used in writing formulas and equations. They allow scientists and students to quickly communicate complex chemical compositions and reactions. Chemical symbols are often accompanied by numbers or signs to represent isotopes, ions, or states of matter.

Ionic Charge

Ionic charge arises when an atom loses or gains electrons, becoming an ion. In a neutral atom, the number of protons equals the number of electrons. However, when an atom like cesium loses an electron, it becomes positively charged because it has more protons than electrons.

In this exercise, the cesium isotope loses one electron, resulting in a cation with a positive charge of +1. This is denoted as Cs⁺, indicating the loss of an electron. It's crucial to know the ionic charge for understanding chemical reactions and bonding, as ions interact based on their charges. Positive ions (cations) will attract negative ions (anions) to form compounds.