Concept: Isotopes are variants of a particular chemical element. Understanding their definition is key.
Step 1: Defining Isotopes
Isotopes of an element are atoms that have:
The same number of protons (which means they have the same atomic number, \(Z\)). Since they have the same number of protons, they are atoms of the same element.
A different number of neutrons.
Because they have a different number of neutrons (but the same number of protons), they will have a different mass number (\(A = Z + \text{neutrons}\)).
Step 2: Analyzing the properties based on the definition
Chemical Properties: Chemical properties are primarily determined by the number of electrons, specifically the valence electrons. Since isotopes of an element have the same number of protons, their neutral atoms have the same number of electrons and the same electron configuration. Therefore, isotopes of an element generally have very similar (nearly identical) chemical properties.
Physical Properties: Some physical properties, particularly those dependent on mass (like density, diffusion rate, melting/boiling points to a very slight extent), can differ slightly between isotopes due to the difference in mass number. So, they do not have exactly the same physical properties, though the differences might be small.
Atomic Number: By definition, isotopes of the same element have the same atomic number (same number of protons).
Number of Neutrons: By definition, isotopes of the same element have a different number of neutrons.
Step 3: Evaluating the options
(1) The same physical properties: Incorrect. Physical properties dependent on mass can differ slightly.
(2) different chemical properties: Incorrect. They have nearly identical chemical properties because they have the same electron configuration.
(3) different number of neutrons: Correct. This is the defining characteristic of isotopes of an element.
(4) different atomic number: Incorrect. They have the same atomic number (same number of protons).
Therefore, isotopes of an element have a different number of neutrons.