Which of the following nuclear reactions will generate an isotope?

An isotope is defined as a nuclide having the same atomic number $$Z$$ (same element) but a different mass number $$A$$. Therefore, in any nuclear reaction that produces an isotope, $$Z$$ must remain unchanged while $$A$$ must change.

Case A: Neutron particle emission
A free neutron leaves the nucleus:
$$^{A}_{Z}X \;\rightarrow\; ^{A-1}_{Z}X \;+\; ^{1}_{0}n$$
• Atomic number: $$Z$$ remains the same.
• Mass number: decreases by 1 (from $$A$$ to $$A-1$$).
Hence the daughter nuclide is the isotope of the parent element.

Case B: Positron ( $$\beta^{+}$$ ) emission
A proton converts into a neutron and emits a positron:
$$^{A}_{Z}X \;\rightarrow\; ^{A}_{Z-1}Y \;+\; ^{0}_{+1}\beta$$
• Atomic number: decreases by 1.
• Mass number: unchanged.
Different element → not an isotope.

Case C: $$\alpha$$-particle emission
An $$\alpha$$ particle ($$^{4}_{2}\mathrm{He}$$) is emitted:
$$^{A}_{Z}X \;\rightarrow\; ^{A-4}_{Z-2}Y \;+\; ^{4}_{2}\alpha$$
• Atomic number: decreases by 2.
• Mass number: decreases by 4.
Different element → not an isotope.

Case D: $$\beta^{-}$$ (electron) emission
A neutron converts into a proton and emits an electron:
$$^{A}_{Z}X \;\rightarrow\; ^{A}_{Z+1}Y \;+\; ^{0}_{-1}\beta$$
• Atomic number: increases by 1.
• Mass number: unchanged.
Different element → not an isotope.

Only neutron emission keeps $$Z$$ unchanged while altering $$A$$, thus producing an isotope of the same element.

Final Answer: Option A which is: neutron particle emission