Problem 33 - General Chemistry: Principles and Modern Applications

Question

Which of the following species has (a) equal numbers of neutrons and electrons; (b) protons, neutrons, and electrons in the ratio 9: 11: 8 ; (c) a number of neutrons equal to the number of protons plus one-half the number of electrons? \(^{24} \mathrm{Mg}^{2+},^{47} \mathrm{Cr},^{60} \mathrm{Co}^{3+},^{35} \mathrm{Cl}^{-},^{124} \mathrm{Sn}^{2+},^{226} \mathrm{Th},^{90} \mathrm{Sr}\)

Step-by-Step Solution

Answer

The atom with equal numbers of neutrons and electrons is \(^{24} \mathrm{Mg}^{2+}\). The atom that has protons, neutrons, and electrons in the ratio 9:11:8 is \(^{60} \mathrm{Co}^{3+}\). The atom that has a number of neutrons equal to the number of protons plus one-half the number of electrons is \(^{35} \mathrm{Cl}^{-}\).

Step 1: Identify numbers for each atom

Firstly, identify the number of protons, neutrons, and electrons for each of the given species. For instance, for \(^{24}Mg^{2+}\), the atomic number of Mg (Magnesium) is 12, so it has 12 protons. It has \(24 - 12 = 12\) neutrons, and since it is a cation with charge \(2+\), it has \(12 - 2 = 10\) electrons.

Step 2: Solve part (a)

For part (a), you have to find an atomic species with equal numbers of neutrons and electrons. Check which among the identified species has got an equal number of neutrons and electrons.

Step 3: Solve part (b)

For part (b), find an atomic species that has protons, neutrons, and electrons in the ratio 9:11:8. By comparing the numbers derived above, find out the species which has a 9:11:8 relation among protons, neutrons and electrons.

Step 4: Solve part (c)

For part (c), find an atomic species in which the number of neutrons is equal to the number of protons plus half of the electrons. By using the results derived from step 1, find out the species that holds true for this condition.

Key Concepts

Protons

Protons are subatomic particles found in the nucleus of every atom. They are positively charged and play a crucial role in defining the atomic number, which determines the identity of an element. When you look at the periodic table, the number of protons is the atomic number listed for each element. For example, magnesium has an atomic number of 12, meaning it has 12 protons.

• Key feature: Positively charged
• Determines the atomic number
• Located in the atomic nucleus

Understanding protons helps us recognize element properties and changes in atomic identity. It’s important to know that protons remain constant in isolated atoms unless there is a nuclear reaction, ensuring the element stays the same.

Neutrons

Neutrons are subatomic particles that reside in the atomic nucleus along with protons. Unlike protons, they carry no electrical charge. Neutrons are essential for the stability of the nucleus as they help offset the repulsive forces between positively charged protons.

The number of neutrons can vary in atoms of the same element, leading to different isotopes. For instance, if we consider the example of magnesium again, while all magnesium atoms have 12 protons, the number of neutrons could vary. For instance, the isotope of magnesium with a mass number of 24 would have 12 neutrons since the formula for calculating it is: Mass Number = Protons + Neutrons.

• Key feature: No electrical charge
• Provides stability to the nucleus
• Responsible for isotopic variation

Neutrons play a vital role in nuclear reactions and atomic stability, making them crucial to atomic structure.

Electrons

Electrons are negatively charged subatomic particles that orbit around the nucleus of an atom. Unlike protons and neutrons, electrons are not confined within the nucleus. Their primary role is in chemical bonding and electrical conductivity. Electrons occupy areas of space called electron shells or energy levels, and they are responsible for the atom's reactivity.

When calculating electrons in ions, like the magnesium ion mentioned initially, it's vital to account for the charge of the ion. For a cation such as Mg\(^{2+}\), you subtract from the number of protons to determine the electrons: 12 - 2 = 10 electrons.

• Key feature: Negatively charged
• Found in electron shells around the nucleus
• Crucial for chemical bonding

Electrons determine how atoms interact with each other, shaping the vast array of chemical compounds we see in nature.