Question

The isotope of an unknown element, \(\mathrm{X},\) has a mass number of 79\. The most stable ion of this isotope has 36 electrons and has a \(2-\) charge. Which of the following statements is(are) true? For the false statements, correct them. a. This ion has more electrons than protons in the nucleus. b. The isotope of \(X\) contains 38 protons. c. The isotope of \(X\) contains 41 neutrons. d. The identity of \(\mathrm{X}\) is strontium, \(\mathrm{Sr}\).

Short answer

The corrected statements are: a. This ion has more electrons than protons in the nucleus (True). b. The isotope of X contains 34 protons. c. The isotope of X contains 45 neutrons. d. The identity of X is Selenium, Se.

Step-by-step solution

Determine the number of electrons, protons, and neutrons in the isotope

First, let's determine the number of electrons in the neutral atom of the isotope. Since its ion has a 2- charge and has 36 electrons, the neutral atom must have 2 less electrons than the ion. Therefore, the number of electrons in the neutral atom is \(36 - 2 = 34\). Now, since the number of electrons is equal to the number of protons in the neutral atom, the number of protons in the isotope is 34. Next, we need to determine the number of neutrons present in the isotope. We know that the mass number (the sum of protons and neutrons) is 79. Therefore, the number of neutrons is determined by subtracting the number of protons from the mass number: \(79 - 34 = 45\).

Check the given statements and correct if necessary

Now, let's check the given statements based on the information we have gathered. a. This ion has more electrons than protons in the nucleus. - Since the ion has 36 electrons and the isotope has 34 protons, this statement is TRUE. b. The isotope of X contains 38 protons. - We have determined that the isotope contains 34 protons, so this statement is FALSE. Correction: The isotope of X contains 34 protons. c. The isotope of X contains 41 neutrons. - Since the isotope contains 45 neutrons, this statement is FALSE. Correction: The isotope of X contains 45 neutrons. d. The identity of X is strontium, Sr. - To verify this statement, we should check the element with 34 protons on the periodic table. The element with 34 protons is Selenium (Se), not Strontium (Sr). Thus, this statement is FALSE. Correction: The identity of X is Selenium, Se.

Summary:

So the corrected statements are: a. This ion has more electrons than protons in the nucleus (True). b. The isotope of X contains 34 protons. c. The isotope of X contains 45 neutrons. d. The identity of X is Selenium, Se.

Key concepts

Atomic Structure

When we delve into atomic structure, we find ourselves at the core of chemistry and physics. In simple terms, atoms are the building blocks of all matter. Each atom consists of a nucleus, containing positively charged protons and neutral neutrons, surrounded by a cloud of negatively charged electrons. The number of protons in the nucleus is the atomic number, which is unique to each element and defines the substance.

The mass number of an atom is the total count of protons and neutrons, giving a perspective on the atom's overall size. In the context of isotopes, although the number of protons remains consistent, thus ensuring the identity of the element is unchanged, the number of neutrons can vary. This variation leads to different isotopes of the same element, each with its unique mass number. For example, an unknown element X with a mass number of 79 and 34 protons will have 45 neutrons. In exercises, to find the number of neutrons, you subtract the atomic number from the mass number, which in our case was 79 - 34 = 45.

Understanding the atomic structure is crucial for interpreting the properties of an element as well as predicting how it will react with others. It's the disparities in the atomic structure that dictate the uniqueness of isotopes and, subsequently, their distinct physical and chemical behaviors.

Ions and Isotopes

The concepts of ions and isotopes are pivotal in grasping the nuances of atomic variations. Starting with ions, these are atoms that have gained or lost electrons. This gain or loss leads to a net charge, rendering the atom an ion. If electrons are lost, the ion is positively charged (known as a cation), whereas if electrons are gained, it bears a negative charge (a.k.a., an anion). In our example, the unknown element X forms a stable ion with a 2- charge by acquiring two additional electrons to the neutral atom's electron configuration.

Isotopes, on the other hand, are variations of the same element that differ in the number of neutrons. These differences do not affect the charge of the atom but do influence properties like stability and radioactive decay. The isotope discussed in the exercise had 45 neutrons, which, combined with the 34 protons, gave it a mass number of 79. It's insightful to realize that the number of protons, which equals the number of electrons in a neutral atom, anchors the element's identity, while the neutrons offer a playfield for isotopic diversity.

Periodic Table

The periodic table is a magnificent tool that organizes all known elements based on their atomic numbers and properties into a coherent framework. It is divided into rows called periods and columns known as groups or families. Elements in the same group generally exhibit similar chemical behaviors due to having the same number of valence electrons.

For isotope identification and elemental analysis, the periodic table is invaluable. Each element in the table is represented by its atomic number (the number of protons in its nucleus) and its chemical symbol. In the corrected statement of the provided solution, it was determined that the unknown isotope belongs to the element with 34 protons. On the periodic table, the element corresponding to this atomic number is Selenium (Se), not Strontium (Sr). Additionally, the table provides information about atomic mass and the structure of electron shells, which is crucial when predicting an element's reactivity and the types of ions it might form. Understanding how to navigate the periodic table is essential for any student of science and helps in making sense of the microscopic world.