In solid state chemistry, carbon, diamond and graphite represent different forms of the same element. Together these different forms are called what?

Introduction / Context:
Elements can sometimes exist in more than one physical form in the same physical state. These different forms may have very different properties even though they consist of the same element. For carbon, well known examples include diamond, graphite, and amorphous carbon. This question asks for the correct term used in chemistry to describe such different forms of the same element in the same state, using carbon, diamond, and graphite as examples.

Given Data / Assumptions:

• All the substances mentioned, carbon, diamond, and graphite, are composed only of the element carbon.
• They differ in structure, hardness, electrical conductivity, and other physical properties.
• The question is about the classification of these forms, not about their detailed structures.
• The options include terms such as isomers, isotopes, allotropes, and isomorphs.

Concept / Approach:
Allotropy is the phenomenon in which an element exists in two or more different structural forms in the same physical state. Each individual form is called an allotrope. For carbon, diamond and graphite are classic allotropes, with diamond having a three dimensional tetrahedral network and graphite having layered sheets of hexagonally arranged carbon atoms. Isomers refer to different compounds with the same molecular formula, isotopes refer to atoms of the same element with different numbers of neutrons, and isomorphs refer to crystals with similar forms but different compositions. Therefore, the correct term for carbon, diamond, and graphite taken together is allotropes.

Step-by-Step Solution:
Step 1: Recognise that the substances listed are all forms of carbon: diamond is a crystalline form, graphite is another crystalline form, and amorphous carbon is yet another. Step 2: Recall the definition of allotropy as different structural forms of the same element in the same physical state. Step 3: Match this definition with the situation of carbon, diamond, and graphite, confirming that they are allotropes. Step 4: Compare the other terms: isomers, isotopes, and isomorphs, and see that they do not describe forms of a single element in the same state. Step 5: Select allotropes as the correct term for the collective description of these forms of carbon.

Verification / Alternative check:
Textbooks in inorganic chemistry list several elements that show allotropy, including carbon, sulfur, phosphorus, and oxygen. For carbon, they specifically mention diamond, graphite, and sometimes fullerenes and nanotubes as allotropes. These descriptions emphasise that the atoms are the same element but arranged in different structures, leading to very different properties such as hardness, electrical conductivity, and optical behaviour. Since the definition matches perfectly with the forms given in the question, the term allotropes is clearly correct.

Why Other Options Are Wrong:
Isomers are different compounds with the same molecular formula, typically associated with organic molecules, not with different elemental forms. Isotopes are atoms of the same element that differ in neutron number and atomic mass, such as carbon 12 and carbon 14, and are not used to describe diamond versus graphite. Isomorphs are crystals of different substances that have similar external forms or structures, not different forms of the same element. None of these terms correctly describes carbon, diamond, and graphite as different structural forms of the same element in the same state.

Common Pitfalls:
Students sometimes confuse isotopes and allotropes because both words start with similar letters and refer to variations related to an element. Another pitfall is to think that any different form of a substance must be an isomer, even when dealing with elements rather than compounds. To avoid these errors, remember that allotropes refer to different structural forms of the same element in one physical state, while isotopes differ in mass and isomers differ in connectivity or arrangement of atoms within compounds. With this distinction clear, it is easy to recognise diamond and graphite as allotropes of carbon.

Final Answer:
Carbon, diamond, and graphite are different structural forms of the same element and are collectively called allotropes of carbon.