Question

How many protons and neutrons are contained in the nucleus of each of the following atoms? For an atom of the element, how many electrons are present? a. \(\quad \frac{63}{29} \mathrm{Cu}\) b. \(\frac{80}{35}\) Bi c. \(_{12}^{24} \mathrm{Mg}\)

Short answer

For the given atoms: a. In \(\frac{63}{29} \mathrm{Cu}\), there are 29 protons, 34 neutrons, and 29 electrons. b. In \(\frac{80}{35}\) Bi, there are 35 protons, 45 neutrons, and 35 electrons. c. In \(_{12}^{24}\mathrm{Mg}\), there are 12 protons, 12 neutrons, and 12 electrons.

Step-by-step solution

a. \(\frac{63}{29} \mathrm{Cu}\)

For this atom of Copper (Cu), the atomic number (Z) is 29 and the mass number (A) is 63. 1. To find the number of protons, we look at the atomic number: \(Z=29\). Thus, there are 29 protons in the nucleus. 2. To find the number of neutrons, we subtract the number of protons from the mass number: \(N=A-Z=63-29=34\). So, there are 34 neutrons in the nucleus. 3. Since there are 29 protons and the atom is electrically neutral, there must be 29 electrons in the atom.

b. \(\frac{80}{35}\) Bi

For this atom of Bismuth (Bi), the atomic number (Z) is 35 and the mass number (A) is 80. 1. To find the number of protons, we look at the atomic number: \(Z=35\). Thus, there are 35 protons in the nucleus. 2. To find the number of neutrons, we subtract the number of protons from the mass number: \(N=A-Z=80-35=45\). So, there are 45 neutrons in the nucleus. 3. Since there are 35 protons and the atom is electrically neutral, there must be 35 electrons in the atom.

c. \(_{12}^{24}\mathrm{Mg}\)

For this atom of Magnesium (Mg), the atomic number (Z) is 12 and the mass number (A) is 24. 1. To find the number of protons, we look at the atomic number: \(Z=12\). Thus, there are 12 protons in the nucleus. 2. To find the number of neutrons, we subtract the number of protons from the mass number: \(N=A-Z=24-12=12\). So, there are 12 neutrons in the nucleus. 3. Since there are 12 protons and the atom is electrically neutral, there must be 12 electrons in the atom.

Key concepts

Protons

Protons are positively charged particles found in the nucleus of an atom. Every atom of a given element has a specific number of protons, which defines its identity. For example, copper (\( \text{Cu} \)) atoms always have 29 protons. The number of protons in an atom is given by the atomic number, represented by the symbol \( Z \).
For instance:

• The atomic number of copper is 29.
• The atomic number of bismuth is 35.
• The atomic number of magnesium is 12.

The atomic number is crucial because it determines the element's position on the periodic table. The more protons an atom has, the heavier it usually is. Additionally, in a neutral atom, the number of protons equals the number of electrons, balancing the positive and negative charges. This makes the atom electrically neutral.

Neutrons

Neutrons are neutral particles that reside in the nucleus alongside protons. They do not have an electric charge and contribute to the mass of an atom. Neutrons, along with protons, determine the isotope of an element. The number of neutrons in an atom is not fixed and can vary even among atoms of the same element.
To find the number of neutrons in an atom, you subtract the atomic number from the mass number:\[ \text{Number of neutrons} = A - Z \]Where \( A \) is the mass number and \( Z \) is the atomic number.

• Copper has 34 neutrons, calculated as \( 63 - 29 = 34 \).
• Bismuth has 45 neutrons, calculated as \( 80 - 35 = 45 \).
• Magnesium has 12 neutrons, calculated as \( 24 - 12 = 12 \).

Electrons

Electrons are negatively charged particles that orbit the nucleus in various energy levels or shells. In a neutral atom, the number of electrons equals the number of protons, ensuring that the atom has an overall neutral charge.
Electrons are responsible for most of the chemical behavior of an atom. They are involved in bonding, reactions, and other processes that define the atom's interactions with other elements.

• Copper has 29 electrons, matching its 29 protons.
• Bismuth has 35 electrons, also equal to its number of protons.
• Magnesium has 12 electrons, equalizing its 12 protons.

The distribution of electrons in various energy levels can affect the atom's properties, making some elements more reactive than others.

Atomic Number

The atomic number of an element is a fundamental property that determines its position on the periodic table. It's denoted by the letter \( Z \) and equals the number of protons in an atom's nucleus. Knowing the atomic number is essential for identifying the element.
For instance:

• The atomic number of copper (\( \text{Cu} \)) is 29.
• The atomic number of bismuth (\( \text{Bi} \)) is 35.
• The atomic number of magnesium (\( \text{Mg} \)) is 12.

Each element on the periodic table has a unique atomic number. This number not only identifies the element but also determines its chemical properties and position in the periodic table. It is crucial for understanding how elements interact and form compounds.

Mass Number

The mass number of an atom is the total number of protons and neutrons in its nucleus. It's denoted by the symbol \( A \) and provides an approximation of the atom's mass since electrons contribute negligibly to the overall mass.
The mass number can vary among isotopes of the same element due to different numbers of neutrons:

• Copper's mass number is 63.
• Bismuth's mass number is 80.
• Magnesium’s mass number is 24.

To find the mass number, you sum the protons and neutrons:\[ A = Z + ext{Neutrons} \]Knowing the mass number helps in determining the element's isotope and is crucial in nuclear chemistry and physics. Understanding this concept allows students to calculate the number of neutrons and to predict the relative stability of an atom.