For an uncharged (electrically neutral) atom, which of the following relationships between subatomic particles is always true?

Introduction / Context:
Atomic structure involves three main subatomic particles: protons, neutrons, and electrons. Understanding how these particles are arranged and how they determine the properties of an atom is fundamental in chemistry and physics. One important concept is electrical neutrality, which describes an atom with no net electric charge. This question asks you to identify which relationship between these particles always holds true for a neutral atom.

Given Data / Assumptions:

• Protons carry a positive charge of plus one unit.
• Electrons carry a negative charge of minus one unit.
• Neutrons carry no electric charge.
• A neutral atom has total positive charge equal to total negative charge.
• Atomic number equals the number of protons; atomic mass equals the sum of protons and neutrons.

Concept / Approach:
For an atom to be electrically neutral, the total positive charge must be balanced by an equal amount of negative charge. Since protons are positively charged and electrons are negatively charged with equal magnitude of charge, neutrality requires that the number of protons equal the number of electrons. Neutrons do not affect electrical charge, although they contribute to the atomic mass and affect nuclear stability. The relationships involving atomic mass, neutrons, or equal protons and neutrons are not universally true for all atoms.

Step-by-Step Solution:
Step 1: Define electrical neutrality. A neutral atom has net charge zero, so the sum of positive and negative charges must be zero. Step 2: Recall that protons have charge plus one and electrons have charge minus one, while neutrons have zero charge. Step 3: For net charge to be zero, the number of positive charges (protons) must equal the number of negative charges (electrons). Step 4: Recognise that this equality does not involve neutrons, so the number of neutrons can vary independently without affecting electric charge. Step 5: Conclude that the only relationship that always holds for a neutral atom is that the number of protons equals the number of electrons.

Verification / Alternative check:
Look at specific examples. A neutral carbon atom has 6 protons and 6 electrons, but it can have 6, 7, or 8 neutrons in different isotopes; all are neutral because protons and electrons match. Sodium has 11 protons and 11 electrons in the neutral atom; when it loses one electron, it forms Na plus, a cation with more protons than electrons. These examples show that neutrality depends only on protons and electrons, not on neutrons. Meanwhile, atomic mass is not equal to atomic number, except in special cases like hydrogen 1, so the other relationships do not hold in general.

Why Other Options Are Wrong:
The atomic mass is equal to the sum of protons and neutrons, not the atomic number, so statement A is false except for very special isotopes. Statement B, that the number of electrons equals the number of neutrons, is not generally true; for instance, oxygen 16 has 8 electrons and 8 neutrons in one isotope, but other elements like chlorine or sodium do not follow such a pattern. Statement D, that atomic mass equals number of electrons, is clearly incorrect except in trivial cases. Statement E, that the number of protons equals the number of neutrons, is not always true; many elements have more neutrons than protons in their stable isotopes.

Common Pitfalls:
Students sometimes confuse atomic number and mass number and may think that atomic mass and atomic number are often equal. Another common mistake is to assume that stable atoms must have equal numbers of protons and neutrons, which is only true for some light elements. To avoid such misconceptions, keep in mind that atomic number equals protons, mass number equals protons plus neutrons, and neutrality is about balancing positive and negative charges, so it depends on protons and electrons only.

Final Answer:
For an uncharged neutral atom, the always true relationship is that the number of protons is equal to the number of electrons.