Problem 7 - University Physics with Modern Physics

Question

The mass of an atom (atomic mass) is equal to a) the sum of the masses of the protons. b) the sum of the masses of protons and neutrons. c) the sum of the masses of protons, neutrons and electrons. d) the sum of the masses of protons, neutrons, and electrons minus the atom's binding energy.

Step-by-Step Solution

Answer

a) The sum of the masses of the protons b) The sum of the masses of protons and neutrons c) The sum of the masses of protons, neutrons, and electrons d) The sum of the masses of protons, neutrons, and electrons minus the atom's binding energy Answer: c) The sum of the masses of protons, neutrons, and electrons

Step 1: Analyze option a

Option a states that the atomic mass is equal to the sum of the masses of the protons. While protons do contribute to the atomic mass, this option does not take into consideration the mass of neutrons and electrons, which are also important components of an atom. Therefore, option a is not correct.

Step 2: Analyze option b

Option b states that the atomic mass is equal to the sum of the masses of protons and neutrons. This option is more accurate than option a because it considers both protons and neutrons, which are the main contributors to the atomic mass. However, it still does not take into account the mass of electrons. Electrons have a smaller mass compared to protons and neutrons but still contribute to the atomic mass. Therefore, option b is closer to the correct answer but not complete.

Step 3: Analyze option c

Option c states that the atomic mass is equal to the sum of the masses of protons, neutrons and electrons. This option is the most accurate because it takes into account all three components of an atom. Protons and neutrons contribute the most to the atomic mass as they are more massive compared to electrons. However, the mass of electrons is still important in calculating the atomic mass. Therefore, option c is the correct answer.

Step 4: Analyze option d

Option d states that the atomic mass is equal to the sum of the masses of protons, neutrons, and electrons minus the atom's binding energy. This option is incorrect because the binding energy is not a mass and should not be included in the calculation of the atomic mass. Binding energy represents the energy required to separate the protons and neutrons in the nucleus of an atom. Therefore, option d is not correct.

Step 5: Conclusion

The atomic mass of an atom is equal to the sum of the masses of protons, neutrons and electrons, which is described in option c.

Key Concepts

Protons

Protons are fundamental components of an atom, found in the nucleus at the center. They carry a positive electrical charge, which balances the negative charge of electrons surrounding the nucleus. The number of protons in an atom defines the element itself, as each element on the periodic table has a unique number of protons, known as its atomic number.

• Atomic Structure: Protons, along with neutrons, make up the nucleus.
• Charge: Each proton carries a positive charge of +1.
• Importance: Protons determine an element's identity and its place on the periodic table.

The mass of a proton is approximately 1 atomic mass unit (amu), making it a significant contributor to the atomic mass of an atom. Without protons, atoms would not hold their distinct identities or their positive charge that attracts electrons.

Neutrons

Neutrons are neutral particles, meaning they carry no electrical charge, and they reside in the atomic nucleus alongside protons. Although they do not influence the chemical behavior of an atom directly in the way protons and electrons do, they play a crucial role in the stability of the nucleus.

• Stability: Neutrons help stabilize the nucleus by offsetting the repulsive forces between positively charged protons.
• Mass Contribution: Like protons, neutrons have a mass close to 1 amu, significantly contributing to the atomic mass.

The presence of neutrons can vary between atoms of the same element. These variations result in isotopes, which are atoms with the same number of protons but different numbers of neutrons. Isotopes have identical chemical properties but differing atomic masses due to the neutron count variations.

Electrons

Electrons are tiny particles with a negative charge that orbit the nucleus in various energy levels. They are much lighter than protons and neutrons but play a vital role in chemical reactions and the overall behavior of an atom.

• Charge: Electrons have a negative charge equal in magnitude to the positive charge of a proton.
• Mass: Their mass is much smaller, approximately 1/1836 of that of a proton or neutron, resulting in a minimal direct contribution to atomic mass.
• Energy Levels: Electrons occupy different energy levels or shells around the nucleus, influencing how atoms interact with each other.

Despite their small mass, electrons are responsible for an atom's chemical properties. They determine how atoms bond and form molecules, as they can be shared, transferred, or pooled between atoms, creating the vast diversity of chemical compounds. Understanding electrons is essential for grasping the concept of atomic mass, even though their direct contribution to it is minor.