Isotopes of an element have (c) different number of neutrons.
Explanation: Isotopes are atoms of the same element with the same number of protons (and therefore the same atomic number) but a different number of neutrons in their nucleus, leading to a difference in mass number.
Why other options are incorrect:
(a) the same physical properties:
While isotopes of an element have the same chemical properties due to the same number of protons and electrons, they do not have the same physical properties. Different numbers of neutrons affect the physical properties like mass, density, and melting/boiling points.
(b) different chemical properties:
Chemical properties are determined by the electron configuration of an atom, which is solely dependent on the number of protons (atomic number). Since isotopes have the same number of protons, they also have the same electron configuration and therefore the same chemical properties.
(d) different atomic numbers:
The atomic number is the number of protons in an atom’s nucleus, and isotopes of an element have the same number of protons, meaning they also have the same atomic number.