Question

An element with mass number 81 contains \(31.7 \%\) more neutrons as compared to protons. Find the symbol of the atom. (a) \({ }_{3}^{81} \mathrm{Se}\) (b) \({ }_{35}^{81} \mathrm{Br}\) (c) \({ }_{36}^{81} \mathrm{Kr}\) (d) \({ }_{37}^{81} \mathrm{Rb}\)

Short answer

The symbol of the atom with mass number 81 and 31.7% more neutrons than protons is \({ }_{35}^{81} \text{Br}\), option (b).

Step-by-step solution

Identify Given Information

The element has a mass number (A) of 81. We know that the number of neutrons is 31.7% more than the number of protons. This information will be used to establish a relationship between the number of protons (Z) and the number of neutrons (N).

Define the Relationship Between Neutrons and Protons

We are given that the number of neutrons is 31.7% more than the number of protons. We can express this relationship mathematically as: \(N = Z + 0.317Z\).

Use the Mass Number to Form an Equation

The mass number A is the sum of the number of protons and the number of neutrons, which can be written as \(A = Z + N\). Using the relationship from Step 2, we can substitute to get: \(81 = Z + (Z + 0.317Z)\).

Solve for the Number of Protons (Z)

Solving for Z we get \(81 = Z + Z + 0.317Z\), which simplifies to \(81 = 2.317Z\). Dividing both sides by 2.317 gives us \(Z = \frac{81}{2.317}\), which calculates to approximately 34.958, rounded to the nearest whole number: 35.

Confirm the Atomic Symbol

With the number of protons determined to be 35, we reference the periodic table to find that the element with 35 protons is Bromine (Br). Thus, the symbol of the atom is \({ }_{35}^{81} Br\).

Key concepts

Atomic Structure

Understanding the atomic structure is essential when learning about chemistry and physics. At its simplest level, an atom consists of a nucleus and an electron cloud. The nucleus, positioned at the center of an atom, contains two kinds of subatomic particles: protons, which have a positive electric charge, and neutrons, which have no charge. Protons and neutrons are collectively known as nucleons.

Electrons, which have a negative charge, orbit the nucleus at various energy levels. The number of protons in the nucleus, also known as the atomic number (Z), uniquely identifies an element and determines its position on the periodic table. For example, if an atom has an atomic number of 6, it is carbon because carbon is the sixth element on the periodic table.

The mass number (A) of an atom is the total number of protons and neutrons in the nucleus. This is significant because it accounts for the majority of the atom's mass. An atom's mass number is not listed on the periodic table, but it can often be deduced or needs to be calculated based on the context of the problem, such as the exercise we're discussing.

Periodic Table

The periodic table is a tabular arrangement of all known chemical elements, arranged by their atomic number, electron configurations, and recurring chemical properties. Elements are organized in rows by their increasing atomic number in the periodic table, also known as periods, and columns known as groups or families, which contain elements with similar chemical behaviors.

One of the most powerful aspects of the periodic table is its predictive ability. Not only does it classify elements, but it also allows us to make predictions about their properties and behaviors. When trying to determine the symbol of an unknown atom, as seen in the exercise, the atomic number plays a crucial role in finding the right element on the periodic table. In the case provided, once the atomic number is calculated, one simply has to locate the element with that atomic number on the table to determine its symbol.

Chemical Elements

Chemical elements are defined as pure substances consisting only of atoms with the same number of protons in their nuclei. They represent the simplest form of matter that cannot be broken down into two or more substances using chemical methods. The periodic table contains a total of 118 confirmed elements, each with unique properties and atomic structures.

Elements are represented by one or two-letter symbols based on their Latin or English names. For instance, 'H' stands for hydrogen, 'O' for oxygen, and 'Fe' for iron (from its Latin name 'ferrum'). In our working exercise, solving for the number of protons led us to determine that the element with 35 protons is Bromine, hence, its symbol is Br. The use of symbols makes it easier to represent elements in chemical equations and share information across languages and regions.