Question

Give the number of protons, neutrons, and electrons in the following isotopes. (a) \({ }^{63} \mathrm{Cu}\) (b) \({ }^{32} \mathrm{~S}\) (c) manganese-55 ( \(\left.{ }^{55} \mathrm{Mn}\right)\) (d) potassium-39 \(\left({ }^{39} \mathrm{~K}\right)\)

Short answer

a) Protons: 29, Neutrons: 34, Electrons: 29; b) Protons: 16, Neutrons: 16, Electrons: 16; c) Protons: 25, Neutrons: 30, Electrons: 25; d) Protons: 19, Neutrons: 20, Electrons: 19.

Step-by-step solution

- Understanding Isotopes

Isotopes are variants of a particular chemical element which differ in neutron number, while retaining the same number of protons. The number of protons is the atomic number (Z), while the number of protons plus neutrons gives the mass number (A). Electrons in a neutral atom equal the number of protons.

- Identifying Atomic Numbers

Refer to the periodic table to find the atomic numbers for each element. Copper (Cu) has an atomic number of 29, sulfur (S) has an atomic number of 16, manganese (Mn) has an atomic number of 25, and potassium (K) has an atomic number of 19.

- Calculating Neutrons for Cu}

For Cu, A = 63 and Z = 29. The number of neutrons is A - Z, so there are 63 - 29 = 34 neutrons.

- Calculating Neutrons for S}

For S, A = 32 and Z = 16. The number of neutrons is A - Z, so there are 32 - 16 = 16 neutrons.

- Calculating Neutrons for Mn}

For Mn, A = 55 and Z = 25. The number of neutrons is A - Z, so there are 55 - 25 = 30 neutrons.

- Calculating Neutrons for K}

For K, A = 39 and Z = 19. The number of neutrons is A - Z, so there are 39 - 19 = 20 neutrons.

- Determining Number of Electrons

For neutral atoms, the number of electrons equals the number of protons. Hence, the electrons for each are Cu: 29, S: 16, Mn: 25, and K: 19.

Key concepts

Atomic Number

The atomic number, often represented with the symbol 'Z', is a fundamental property of an atom. It indicates the number of protons found in the nucleus of an atom. Since protons are positively charged, the atomic number also determines the electrical charge of the nucleus.

Every element on the periodic table is uniquely defined by its atomic number. For instance, hydrogen has an atomic number of 1, meaning all hydrogen atoms have exactly one proton in their nucleus. The atomic number is crucial because it not only identifies the element but also its chemical behavior. In the context of isotopes, despite variations in neutron numbers, the atomic number remains consistent across all isotopes of a particular element, ensuring the chemical identity is preserved.

Neutrons in Isotopes

Isotopes are characterized by the variation in the number of neutrons they possess. While the number of protons (and thus the atomic number) remains unchanged, different isotopes of the same element have different mass numbers due to these additional (or fewer) neutrons. Neutrons are neutrally charged particles and contribute significantly to the mass of an atom.

To calculate the number of neutrons in an isotope, you subtract the atomic number (Z) from the mass number (A): Number of Neutrons = Mass Number (A) - Atomic Number (Z). As seen in the exercise solutions, for Copper-63, the atomic number is 29 and the mass number is 63, so the number of neutrons is 34.

Protons and Electrons in Atoms

In every atom, the number of protons determines the number of electrons, provided that the atom is neutral, meaning it has no overall electrical charge. This is due to the fact that protons and electrons carry opposite but equal charges. Each proton’s positive charge is balanced by an electron’s negative charge.

For example, a neutral atom of copper (Cu), which has an atomic number of 29, will therefore have 29 protons in its nucleus and 29 electrons orbiting the nucleus. If an atom gains or loses electrons, it becomes an ion, which is a charged species. In the solutions provided, all atoms considered were neutral, so the number of electrons was equal to the atomic number.

Mass Number

The mass number, represented by 'A', is the total number of protons and neutrons in an atom's nucleus. Since protons and neutrons have roughly the same mass (and electrons have a much smaller mass), the mass number approximately equals the atomic mass of the atom. However, it must be noted that mass number is a whole number, while atomic masses can be fractional due to the presence of isotopes.

For instance, sulfur (S) with a mass number of 32 has 16 protons and 16 neutrons. Calculating the mass numbers helps in identifying the isotope of an element and is crucial for understanding nuclear reactions and decay, chemical bonding, and the stability of atoms.