Question

For each of the following species, determine the number of protons and the number of neutrons in the nucleus: \({ }_{2}^{3} \mathrm{He},{ }_{2}^{4} \mathrm{He}_{\mathrm{r}}{ }^{24} \mathrm{Mg},{ }_{1}^{25} \mathrm{Mg},{ }_{2}^{48} \mathrm{Ti}_{15}{ }^{79} \mathrm{Br},{ }^{195} \mathrm{Pt}\)

Short answer

He: 2p, 1n; He: 2p, 2n; Mg: 12p, 12n; Mg: 12p, 13n; Ti: 22p, 26n; Br: 35p, 44n; Pt: 78p, 117n.

Step-by-step solution

Understanding Atomic Symbols

The atomic symbol of an element provides essential information: 1. The first number (lower left) is the atomic number, which is equal to the number of protons. 2. The second number (upper left) is the mass number, which is the sum of protons and neutrons. You can calculate the number of neutrons by subtracting the atomic number from the mass number.

Species 1: _{2}^{3}He

For this isotope of Helium: - Atomic number (number of protons) = 2 - Mass number = 3 So, the number of neutrons = Mass number - Atomic number = 3 - 2 = 1.

Species 2: _{2}^{4}He

For this isotope of Helium: - Atomic number (number of protons) = 2 - Mass number = 4 So, the number of neutrons = Mass number - Atomic number = 4 - 2 = 2.

Species 3: _{12}^{24}Mg

For this isotope of Magnesium: - Atomic number (number of protons) = 12 - Mass number = 24 So, the number of neutrons = Mass number - Atomic number = 24 - 12 = 12.

Species 4: _{12}^{25}Mg

For this isotope of Magnesium: - Atomic number (number of protons) = 12 - Mass number = 25 So, the number of neutrons = Mass number - Atomic number = 25 - 12 = 13.

Species 5: _{22}^{48}Ti

For this isotope of Titanium: - Atomic number (number of protons) = 22 - Mass number = 48 So, the number of neutrons = Mass number - Atomic number = 48 - 22 = 26.

Species 6: _{35}^{79}Br

For this isotope of Bromine: - Atomic number (number of protons) = 35 - Mass number = 79 So, the number of neutrons = Mass number - Atomic number = 79 - 35 = 44.

Species 7: _{78}^{195}Pt

For this isotope of Platinum: - Atomic number (number of protons) = 78 - Mass number = 195 So, the number of neutrons = Mass number - Atomic number = 195 - 78 = 117.

Key concepts

Atomic Number

The atomic number is a fundamental concept in understanding atomic structure. It is represented as the number located at the lower left of an element's atomic symbol. This number tells us the total count of protons present in the nucleus of an atom.
The importance of the atomic number cannot be overstated:

• It defines the identity of an element, meaning no two elements can have the same atomic number.
• It determines the position of the element in the periodic table.
• Since atoms are electrically neutral overall, the atomic number is also equal to the number of electrons in an uncharged atom.

In the example of isotopes \({ }_{2}^{3}\)He and \({ }_{2}^{4}\)He, both have an atomic number of 2, indicating they are forms of the same element, Helium.

Mass Number

The mass number of an atom gives us the total number of particles in its nucleus. This includes both protons and neutrons. It is represented as the number at the upper left of an atomic symbol and is integral in calculating the number of neutrons an atom has.
The difference between mass number and atomic number yields the number of neutrons because:

• Mass Number = Protons + Neutrons
• Neutrons = Mass Number - Atomic Number

For instance, in \({ }_{12}^{25}\)Mg, Magnesium has a mass number of 25 and an atomic number of 12, leading us to calculate 13 neutrons.

Isotopes

Isotopes are variants of a particular chemical element which differ in neutron number, while retaining the same number of protons. They have identical atomic numbers but different mass numbers due to the varying count of neutrons.
This concept is crucial for understanding elements such as:

• Helium isotopes \({ }_{2}^{3}\)He and \({ }_{2}^{4}\)He, where the number of neutrons is 1 and 2, respectively.
• Magnesium isotopes \({ }_{12}^{24}\)Mg and \({ }_{12}^{25}\)Mg, differing by one neutron even though they have the same number of protons.

Isotopes of an element often display similar chemical properties but can have different physical properties due to the difference in mass.

Protons

Protons are positively charged particles found within an atom's nucleus. Their number, which is indicated by the atomic number, is consistent for every atom of an element, defining its identity.
Each element's unique number of protons lays the foundation for:

• The element's chemical behavior, as electrons are equal in number to protons and dictate the atom's interactions.
• The element's place on the periodic table.

For example, the atomic number 79 for \({ }^{195}\)Pt identifies it unequivocally as Platinum.

Neutrons

Neutrons are neutral particles housed in the nucleus of an atom, contributing significantly to its mass but not its charge. Unlike protons, they can vary in number, resulting in isotopes.
The role of neutrons includes:

• Stabilizing the nucleus by offsetting the repulsive forces between positively charged protons.
• Influencing the mass number and, therefore, the atomic mass of isotopes.

By understanding the calculation of neutrons (e.g., 26 in \({ }_{22}^{48}\)Ti), we gain deeper insights into the nuances of atomic structure and isotopic variation.