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(D) Isotopes are atoms of the same element that have the same atomic number but different mass numbers.$(i)$ Incorrect: Isotopes have different atomic

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$(ii)$ and $(iv)$

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(D) Isotopes are atoms of the same element that have the same atomic number but different mass numbers.$(i)$ Incorrect: Isotopes have different atomic masses due to a different number of neutrons.$(ii)$ Correct: Isotopes of the same element must have the same atomic number (number of protons).$(iii)$ Incorrect: Isotopes often show different physical properties (like density or boiling point) because these properties depend on the mass of the atom.$(iv)$ Correct: Isotopes show the same chemical properties because chemical properties are determined by the electronic configuration,which remains the same for isotopes of the same element.Therefore,statements $(ii)$ and $(iv)$ are correct.

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Which of the following are the characteristics of isotopes of an element?$(i)$ Isotopes of an element have same atomic masses$(ii)$ Isotopes of an element have same atomic number$(iii)$ Isotopes of an element show same physical properties$(iv)$ Isotopes of an element show same chemical properties