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Chapter 2: Problem 51

One isotope of a metallic element has a mass number of 65 and has 35 neutrons in the nucleus. The cation derived from the isotope has 28 electrons. Write the symbol for this cation.

Short Answer

Expert verified
The symbol for the cation derived from the given isotope is \( Zn^{2+} \).

Step by step solution

01

Finding the Number of Protons

Since the mass number of an atom is the total amount of protons and neutrons, subtract the number of neutrons from the mass number to get the number of protons. In this case, the calculation is as follows: 65 (mass number) - 35 (neutrons) = 30 protons. So the element has 30 protons in its nucleus.
02

Identifying the Element

By using the periodic table, one can determine that the atom with 30 protons is Zinc. The atomic number of Zinc is 30 which means it normally has 30 electrons. However, in this problem, we are given a cation - an ion with fewer electrons than protons.
03

Writing the Symbol for the Cation

This ion has 28 electrons, which means it has lost 2 electrons and is a cation. The atomic symbol of Zinc is Zn. So, based on the loss of two electrons, the charge of the cation is +2. Therefore, the symbol for this cation is \( Zn^{2+} \).

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Mass Number
When we talk about the mass number, we are referring to the total number of protons and neutrons in an atom's nucleus. It's an essential concept in understanding isotopes because, while the number of protons (atomic number) defines what element an atom is, the number of neutrons can vary. This is what forms different isotopes of the same element.

For example, an isotope with a mass number of 65 has a total of 65 protons and neutrons combined. The exact number of protons and neutrons can be found if either the atomic number or the number of neutrons is known. In this case, with 35 neutrons, you subtract from the mass number to find that there are 30 protons, which also gives you the atomic number of the element.
Atomic Number
The atomic number is foundational to the organization of the periodic table. It's defined as the number of protons found in the nucleus of an atom and determines the chemical properties of an element and its place on the table. Each element has a unique atomic number, so once you know the atomic number, you can correctly identify the element.

For instance, an element with 30 protons has the atomic number 30. Using the periodic table, we can identify this element as Zinc (Zn). The atomic number is also significant because, in a neutral atom, it tells you the number of electrons orbiting the nucleus.
Periodic Table
The periodic table is a marvel of science, organizing all known elements into a tabular display based on their atomic number, electron configurations, and recurring chemical properties. Elements are listed in order of increasing atomic number from left to right and are arranged in rows called periods and columns known as groups or families.

When solving problems involving elements and their ions, the periodic table becomes a crucial tool. It allows us to quickly determine an element's atomic number and its typical properties, such as reactivity or the formation of specific ions like cations or anions. In our example, we used the table to verify that the atomic number 30 corresponds to Zinc (Zn).
Cation Symbol
Cations are positively charged ions, meaning they have more protons than electrons. The symbol for a cation includes the element's symbol from the periodic table, followed by the charge in superscript. The charge is the difference between the number of protons and electrons.

As in our exercise, a Zinc (Zn) cation with 28 electrons (2 less than its atomic number of 30) will have a charge of +2, represented as the symbol with a superscript plus two, or in chemical notation:

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Most popular questions from this chapter

(a) Describe Rutherford's experiment and how it led to the structure of the atom. How was he able to estimate the number of protons in a nucleus from the scattering of the \(\alpha\) particles? (b) Consider the \({ }^{23} \mathrm{Na}\) atom. Given that the radius and mass of the nucleus are \(3.04 \times 10^{-15} \mathrm{~m}\) and \(3.82 \times 10^{-23} \mathrm{~g},\) respectively, calculate the density of the nucleus in \(\mathrm{g} / \mathrm{cm}^{3}\). The radius of a \({ }^{23}\) Na atom is \(186 \mathrm{pm}\). Calculate the density of the space occupied by the electrons in the sodium atom. Do your results support Rutherford's model of an atom? [The volume of a sphere is \((4 / 3) \pi r^{3},\) where \(r\) is the radius. \(]\)

Why is magnesium chloride \(\left(\mathrm{MgCl}_{2}\right)\) not called magnesium(II) chloride?

Give the number of protons and electrons in each of the following common ions: \(\mathrm{K}^{+}, \mathrm{Mg}^{2+}, \mathrm{Fe}^{3+}, \mathrm{Br}^{-},\) \(\mathrm{Mn}^{2+}, \mathrm{C}^{4-}, \mathrm{Cu}^{2+}\)

Ethane and acetylene are two gaseous hydrocarbons. Chemical analyses show that in one sample of ethane, \(2.65 \mathrm{~g}\) of carbon are combined with \(0.665 \mathrm{~g}\) of hydrogen, and in one sample of acetylene, \(4.56 \mathrm{~g}\) of carbon are combined with \(0.383 \mathrm{~g}\) of hydrogen. (a) Are these results consistent with the law of multiple proportions? (b) Write reasonable molecular formulas for these compounds.

Identify each of the following elements: (a) a halogen whose anion contains 36 electrons, (b) a radioactive noble gas with 86 protons, (c) a Group \(6 \mathrm{~A}\) element whose anion contains 36 electrons, (d) an alkali metal cation that contains 36 electrons, (e) a Group 4 A cation that contains 80 electrons.
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