Which of the following are isotopes? $(I)$Atom, whose nucleus contains $20p + 15n$ $(II)$Atom, whose nucleus contains $20p + 17n$ $(III)$Atom, whose nucleus contains $18p + 22n$ $(IV)$ Atom, whose nucleus contains $18p + 21n$ $(1)(I)and(III)$ $(2)(I)and(II)$ $(3)(II)and(III)$ $(4)(III)and(IV)$
Hint: Isotopes are two or more types of atoms that have the same atomic number. Isotopes can either form spontaneously through radioactive decay of a nucleus or artificially by bombarding a stable nucleus with charged particles via accelerators or neutrons in a nuclear reactor.
Complete answer: Isotopes are two or more types of atoms that have the same atomic number (number of protons in their nuclei) and position in the periodic table (and hence belong to the same chemical element), and that differ in nucleon numbers (mass numbers) due to different numbers of neutrons in their nuclei. While all isotopes of a given element have almost the same chemical properties, they have different atomic masses and physical properties. The number of protons within the atom's nucleus is called atomic number and is equal to the number of electrons in the neutral (non-ionized) atom. Each atomic number identifies a specific element, but not the isotope; an atom of a given element may have a wide range in its number of neutrons. The number of nucleons (both protons and neutrons) in the nucleus is the atom's mass number, and each isotope of a given element has a different mass number. So, the correct answer is $(2)(I)$ and $(II)$ and $(4)(III)and(IV)$
Note: Atomic nuclei consist of protons and neutrons bound together by the residual strong force. Because protons are positively charged, they repel each other. Neutrons, which are electrically neutral, stabilize the nucleus in two ways. Their co-presence pushes protons slightly apart, reducing the electrostatic repulsion between the protons, and they exert the attractive nuclear force on each other and on protons.