A sample of matter must be identified as copper if which one of the following conditions is definitely true for every atom in that sample?

Introduction / Context:
This question tests understanding of how elements are defined in modern chemistry. While many properties such as color, reactivity, or melting point are associated with particular elements, the fundamental definition of an element is based on the number of protons in the nucleus of each atom. This number is called the atomic number. Copper has a specific atomic number, and that definition allows us to say with certainty when a sample must be copper.

Given Data / Assumptions:

• We are asked when a sample must be copper.
• One option mentions that each atom has 29 protons.
• Other options mention properties such as reactivity with oxygen, conductivity, melting point, and color.
• We assume standard chemical definitions of atomic number and element identity.

Concept / Approach:
Every element is uniquely defined by its atomic number, which is the number of protons in the nucleus of its atoms. Copper has atomic number 29, meaning each copper atom has 29 protons. While many materials conduct electricity, react with oxygen, or have particular colors, these properties are not unique to copper. Only the proton count provides a certain identification. Therefore, the condition that every atom has 29 protons is the unambiguous test that the sample is copper.

Step-by-Step Solution:

Verification / Alternative check:
Periodic tables show copper with symbol Cu and atomic number 29. Chemistry definitions state that if an atom has atomic number 29, it is copper irrespective of its isotopic mass or chemical state. Experimental methods such as mass spectrometry or nuclear measurements can determine the proton number. No other element shares the same atomic number, so there is a one to one relationship. This confirms that the proton count condition is the correct and precise criterion.

Why Other Options Are Wrong:

• Atoms reacting with oxygen: Many elements form oxides, so this property is not unique to copper.
• Electrical conductivity: Many metals and some solutions conduct electricity; this does not uniquely identify copper.
• Melting at about 1768 K: While the melting point is characteristic, a single measured melting point could be subject to experimental error or alloy formation.
• Reddish brown color: Copper is famous for this color, but surface conditions, alloys, or coatings may change appearance, and color alone is not a fundamental definition.

Common Pitfalls:
Students often rely on familiar visual or practical properties to identify elements in questions. While those properties help in everyday identification, examination questions like this deliberately test conceptual knowledge. The key is to remember that atomic number is the only strict defining property of an element. By focusing on proton number rather than less precise features, you can answer similar questions about identity of elements with confidence.

Final Answer:
A sample must be copper if Each atom in the sample has 29 protons in its nucleus.