Problem 54 - Chemistry: Principles and Reactions

Question

A student saw the following nuclear symbol for an unknown element: \({ }_{11}^{33} \mathrm{X} .\) Which of the following statements about \(\mathrm{X}\) and \({ }_{11}^{23} \mathrm{X}\) are true? (a) \(\mathrm{X}\) is sodium. (b) \(\mathrm{X}\) is vanadium. (c) \(\mathrm{X}\) has 23 neutrons in its nucleus. (d) \(\mathrm{X}^{2+}\) has 13 electrons. (e) \({ }_{11}^{23} \mathrm{X}\) has a proton/neutron ratio of about \(1.1\).

Step-by-Step Solution

Answer

a. X is sodium b. X is vanadium c. X has 23 neutrons in its nucleus d. X²⁺ has 13 electrons e. The isotope ¹¹²³X has a proton/neutron ratio of about 1.1.

Step 1: Identify the given element

The given nuclear symbol is \({}_{11}^{33}\mathrm{X}\). The atomic number is 11, which represents the number of protons, and the mass number (A) is 33, which represents the sum of protons and neutrons. We can identify the element by looking up the atomic number in the periodic table. The element with atomic number 11 is sodium (Na).

Step 2: Evaluate statement (a)

Statement (a) states that \(\mathrm{X}\) is sodium. Since the atomic number of this element is 11, we can confirm that this statement is true.

Step 3: Evaluate statement (b)

Statement (b) states that \(\mathrm{X}\) is vanadium. Since the atomic number of this element is 11, and vanadium has an atomic number of 23, we can confirm that this statement is false.

Step 4: Evaluate statement (c)

Statement (c) states that \(\mathrm{X}\) has 23 neutrons in its nucleus. We can calculate the number of neutrons by subtracting the atomic number (protons) from the mass number (protons + neutrons): \(33 - 11 = 22\). Therefore, this statement is false.

Step 5: Evaluate statement (d)

Statement (d) states that \(\mathrm{X}^{2+}\) has 13 electrons. When an atom has a positive charge, that means it has lost electrons. The original number of electrons in a neutral \(\mathrm{X}\) atom is equal to its atomic number (11). Losing 2 electrons results in 11 - 2 = 9 electrons. Therefore, this statement is false.

Step 6: Evaluate statement (e)

Statement (e) states that \({}_{11}^{23}\mathrm{X}\) has a proton/neutron ratio of about \(1.1\). We can calculate the proton and neutron numbers for \({}_{11}^{23}\mathrm{X}\): - Protons = 11 (atomic number) - Mass Number = 23 - Neutrons = 23 - 11 = 12 Now, we can find the proton/neutron ratio: \(\frac{11}{12} \approx 0.917\), which is not equal to \(1.1\). Therefore, this statement is false. In conclusion, only statement (a) is true.

Key Concepts

The Periodic Table Simplified

The periodic table is not just a grid of elements; it's akin to a comprehensive map of the tiny building blocks that make up our universe. Arranged by increasing atomic number, the table groups elements with similar chemical behaviors into columns, called 'groups'. Along rows, or 'periods', elements display a progression in properties and mass. Each position in the table provides fundamental data about an element, including its atomic number and approximate atomic mass. For students, the periodic table is an invaluable tool for predicting the types of chemical reactions that an element may engage in.

Understanding the periodic table's layout and the significance of the numbers displayed on it is crucial. For instance, the atomic number, located above each element's symbol, reveals the number of protons, and thus, the unique identity of the element. Navigating the periodic table can seem challenging at first, but once familiar with its structure, it becomes a rapid way to glean information about various elements and their properties.

Atomic Number: The Element's ID

Every element has a unique identifier known as the atomic number. It represents the number of protons packed in the nucleus of an atom and is paramount in determining the element's position on the periodic table. Since each element has a different atomic number, this value allows chemists to distinguish one element from another. In an electrically neutral atom, the atomic number also equals the electron count swirling in orbits around the nucleus.

This number isn't random; it defines the very essence of an element. For example, all carbon atoms have 6 protons, symbolized as \( C \). If you alter the proton count, you change the element entirely! Understanding an element’s atomic number is the key to unlocking the predictive powers of the periodic table.

Calculating Neutrons in an Atom

To determine the number of neutrons in an atom, you need two pieces of information: the element's atomic number and its atomic mass number. The atomic mass number is the combined count of protons and neutrons in an atom's nucleus. By subtracting the atomic number (the count of protons) from the atomic mass number, you can pinpoint the neutron count.

For instance, let’s take an element \( _{Z}^{A}X \), where \(Z\) is the atomic number and \(A\) is the atomic mass number. The neutron number \(N\) is found by the simple subtraction: \(N = A - Z\). This calculation is crucial for understanding the make-up of isotopes, which are atoms of the same element that differ in neutron count.

Understanding the Proton/Neutron Ratio

The stability of an atom hinges on the delicate balance between the number of protons and neutrons in its nucleus, known as the proton/neutron ratio. Atoms strive for an optimal ratio for stability, and deviations from this balance can lead to radioactivity.

In lighter elements, a 1:1 ratio is often enough to ensure stability, while heavier elements tend to require more neutrons to offset the increasing repulsion between protons due to their positive charge. The ratio forms the crux of nuclear stability and can be the difference between an enduring molecule and one that emits radiation as it seeks stability. Being able to calculate this ratio, as evident from solving the textbook exercise, provides students with insight into the tendency of an element to undergo radioactive decay.