Question

Indicate the number of protons and neutrons in the following nuclei: (a) \({ }_{22}^{55} \mathrm{Mn},(\mathbf{b}){ }^{201} \mathrm{Hg},(\mathbf{c})\) potassium- \(39 .\)

Short answer

(a) \({}_{22}^{55} \mathrm{Mn}\): 22 protons and 33 neutrons (b) \({}^{201} \mathrm{Hg}\): 80 protons and 121 neutrons (c) Potassium-39: 19 protons and 20 neutrons

Step-by-step solution

Identify the atomic number and mass number

In nuclear notation, the symbol of an atom is represented by ${ }_Z^A \mathrm{X}$, where X is the chemical symbol, Z is the atomic number (number of protons), and A is the mass number (total number of protons and neutrons). (a) \({}_{22}^{55} \mathrm{Mn}\) The atomic number (Z) is 22, and the mass number (A) is 55. (b) For \({}^{201} \mathrm{Hg}\), only the mass number is provided (A=201). We can use the periodic table to find the atomic number (Z) for mercury (Hg). (c) For potassium-39, only the mass number is provided (A=39). We can use the periodic table to find the atomic number (Z) for potassium (K).

Find the atomic number (Z) using the periodic table

In order to find the atomic number for mercury and potassium, consult the periodic table. For mercury (Hg), the atomic number (Z) is 80. For potassium (K), the atomic number (Z) is 19.

Calculate the number of protons and neutrons

We can use the formula: Number of neutrons = Mass number (A) - Atomic number (Z) (a) \({}_{22}^{55} \mathrm{Mn}\): Number of protons = Atomic number (Z) = 22 Number of neutrons = Mass number (A) - Atomic number (Z) = 55 - 22 = 33 (b) \({}^{201} \mathrm{Hg}\): Number of protons = Atomic number (Z) = 80 Number of neutrons = Mass number (A) - Atomic number (Z) = 201 - 80 = 121 (c) Potassium-39: Number of protons = Atomic number (Z) = 19 Number of neutrons = Mass number (A) - Atomic number (Z) = 39 - 19 = 20

Present the results

Now we have all the needed information for given nuclei. (a) \({}_{22}^{55} \mathrm{Mn}\): Number of protons = 22 Number of neutrons = 33 (b) \({}^{201} \mathrm{Hg}\): Number of protons = 80 Number of neutrons = 121 (c) Potassium-39: Number of protons = 19 Number of neutrons = 20

Key concepts

Understanding Atomic Number

Every chemical element on the periodic table has a specific atomic number. The atomic number is fundamental because it tells us the number of protons in an atom's nucleus. This number is designated as "Z" in the atom's notation. For example, hydrogen, the first element, has an atomic number of 1 because there is only one proton in its nucleus.

Here is why the atomic number is important:

• Determines the element's identity: Each element is defined by its atomic number. If you change the number of protons, you change the element.
• Defines the element's position on the Periodic Table: Elements are arranged sequentially based on their atomic numbers.
• Typically equals the number of electrons: In a neutral atom, the number of protons equals the number of electrons, keeping the atom electrically balanced.

This concept was used in the provided problem, where we identified the atomic number for mercury (Hg) as 80 and for potassium (K) as 19.

Mass Number and Its Significance

The mass number, often labeled as "A," represents the total number of protons and neutrons in an atom's nucleus. It's called the mass number because protons and neutrons contribute almost all of the atom's mass; electrons have little mass compared to them.

Why is the mass number significant?

• It provides information about the isotope: Different isotopes of an element have the same number of protons but different numbers of neutrons, leading to different mass numbers.
• Aids in calculating neutrons: By knowing the atomic and mass numbers, you can determine the number of neutrons.

In our example, manganese ( {Mn}) has a mass number of 55, meaning it has 55 protons and neutrons combined. Similarly, for mercury ( {Hg}), the mass number is 201, indicating that together with protons, it has a higher count of subatomic particles.

Calculating Neutrons

Calculating the number of neutrons in an atom is straightforward once you have the mass number and the atomic number. Neutrons do not affect the electric charge of the atom, as they are neutral particles. The formula used for neutron calculation is:

\[ \text{Number of Neutrons} = \text{Mass Number (A)} - \text{Atomic Number (Z)} \]

This calculation is simple yet crucial because it helps us understand isotopes. For instance, the manganese nucleus has 33 neutrons, calculated by 55 (Mass Number) - 22 (Atomic Number). Likewise, to find the number of neutrons in mercury, we use 201 - 80, resulting in 121 neutrons. For potassium-39, the calculation goes 39 - 19, giving us 20 neutrons.

This straightforward subtraction not only reveals the neutron content but also plays a critical role in understanding the composition and stability of different isotopes.