Question

Fill in the gaps in the following table, assuming each column represents a neutral atom: $$ \begin{array}{|l|l|l|l|l|l|} \hline \text { Symbol } & { }^{52} \mathrm{Cr} & & & & \\ \hline \text { Protons } & & 25 & & & 82 \\ \hline \text { Neutrons } & & 30 & 64 & & \\ \hline \text { Electrons } & & & 48 & 86 & \\ \hline \text { Mass no. } & & & & 222 & 207 \\ \hline \end{array} $$

Short answer

The completed table is: $$ \begin{array}{|l|l|l|l|l|l|} \hline \text { Symbol } & { }^{52} \mathrm{Cr} & \mathrm{Mn} & \mathrm{Mn} & \mathrm{Pb} & \mathrm{Pb} \\\ \hline \text { Protons } & 24 & 25 & 25 & 82 & 82 \\\ \hline \text { Neutrons } & 28 & 30 & 64 & 140 & 125 \\\ \hline \text { Electrons } & 24 & 25 & 25 & 82 & 82 \\\ \hline \text { Mass no. } & 52 & 55 & 89 & 222 & 207 \\\ \hline \end{array} $$

Step-by-step solution

Find atomic symbol and number for the missing entries

Using the periodic table, we can find the atomic symbol and atomic number (number of protons) for the missing entries.

Step 1.1: Atomic symbol with 25 protons

25 protons correspond to the element Manganese (Mn).

Step 1.2: Atomic symbol with 82 protons

82 protons correspond to the element Lead (Pb).

Determine the number of protons for the missing entries

From the given atomic symbols, we can refer to the periodic table and find the number of protons for the remaining entries.

Step 2.1: \$^{} \mathrm{Cr}\$ protons

Chromium (Cr) has an atomic number of 24, so it has 24 protons.

Determine the number of neutrons for the missing entries

To find the number of neutrons, we will use the formula: Number of Neutrons = Mass Number - Number of Protons

Step 3.1: Neutrons for element with mass number 222

Number of Neutrons = 222 - 82 (Pb or Lead atomic number) = 140

Step 3.2: Neutrons for element with mass number 207

Number of Neutrons = 207 - 82 (Pb or Lead atomic number) = 125

Determine the number of electrons for the missing entries

In a neutral atom, the number of electrons is equal to the number of protons.

Step 4.1: Electrons for element with 25 protons (Mn)

Number of Electrons = Number of Protons = 25

Step 4.2: Electrons for element with 64 neutrons

64 neutrons in the atom implies this atom has a mass number of \(64 + 25 (Mn or Manganese atomic number) = 89\). This means it is an isotope of Manganese with 25 protons, so the number of electrons is also 25.

Determine the mass number for the missing entries

The mass number is the sum of the number of protons and neutrons.

Step 5.1: Mass number for element with 48 electrons

48 electrons mean this atom has 48 protons, which corresponds to the element Cadmium (Cd). The atom with 64 neutrons implies a mass number of \(48 + 64 = 112\)

Fill the table using the information obtained in previous steps

$$ \begin{array}{|l|l|l|l|l|l|} \hline \text { Symbol } & { }^{52} \mathrm{Cr} & \mathrm{Mn} & \mathrm{Mn} & \mathrm{Pb} & \mathrm{Pb} \\\ \hline \text { Protons } & 24 & 25 & 25 & 82 & 82 \\\ \hline \text { Neutrons } & 28 & 30 & 64 & 140 & 125 \\\ \hline \text { Electrons } & 24 & 25 & 25 & 82 & 82 \\\ \hline \text { Mass no. } & 52 & 55 & 89 & 222 & 207 \\\ \hline \end{array} $$

Key concepts

Periodic Table

Imagine a grand library where elements are books arranged by similarities and differences: that's the periodic table for you. It's a systematic layout of all known chemical elements, ordered by their atomic number, electron configuration, and recurring chemical properties.

Columns, known as groups, and rows, aptly called periods, classify the elements. Groups share chemical characteristics because they have the same number of electrons in their outer shell. Periods display a gradual change in properties across the table from one side to the other. For instance, elements on the left are metals and as we glide to the right, they become less metallic, culminating in non-metals. The periodic table is essential when it comes to solving atomic structure problems like the one provided, as it aids in identifying elements and their properties simply by knowing either their atomic number or symbol.

Atomic Number

A cornerstone piece of information in the atomic world is the atomic number, symbolized as 'Z'. Think of it as the unique identity card for each chemical element. It tells you the count of protons residing in an atom's nucleus and consequently, for neutral atoms, the number of electrons whizzing around it. In our given exercise, we utilized the atomic number to determine the element. For example, an element with an atomic number of 25 is Manganese (Mn). This atomic number is not just a count; it's also an elemental fingerprint, distinguishing each element from another in the periodic table.

Neutrons

Neutrons, the neutral particles nestled in an atom's nucleus alongside protons, are pivotal for isotopic identities and atomic stability. Their count is not indicated directly on the periodic table, which is where the mass number (total of protons and neutrons) comes into play. To find the neutron count, we subtract the number of protons (the atomic number) from the mass number. A careful balance of neutrons to protons contributes to the stability of an atom; too many or too few can lead to the formation of unstable isotopes which can be radioactive. In the exercise, knowing the mass number and the atomic number enabled us to solve for the number of neutrons in an atom, providing us with all the necessary information to understand the atom's core structure.

Isotopes

Isotopes are variations of a single element that have differing numbers of neutrons but the same number of protons. Because they are the same element, they have identical atomic numbers but different mass numbers. An excellent demonstration of isotopes is given in the exercise: Manganese with a mass number of 55 and 89 are both isotopes of Manganese. The physical and chemical properties of isotopes of the same element are quite similar, but their nuclear properties can vary greatly. Isotopes can be stable or unstable, where unstable isotopes are radioactive and have the potential for various applications in medicine, archaeology, and energy production.