Recall the meaning of isotopes

Isotopes are atoms of the same element having:

• same atomic number $Z$
• different mass number $A$

So, for a nuclear reaction to produce an isotope of the original element, the atomic number must remain unchanged while the mass number changes.

Check each type of emission

(A) Neutron emission

A neutron has: $^1_0 n$ If a nucleus emits a neutron:

• mass number decreases by $1$
• atomic number remains the same

Symbolically: $^A_Z X \rightarrow ^{A-1}_Z X + ^1_0 n$

Since $Z$ is unchanged and $A$ changes, the product is an isotope of the same element.

So, A is correct.

(B) Positron emission

In positron emission: $^A_Z X \rightarrow ^A_{Z-1} Y + ^0_{+1} e$

• mass number remains the same
• atomic number decreases by $1$

Since the atomic number changes, the product is a different element, not an isotope of the original one.

So, B is incorrect.

(C) $\alpha$-particle emission

An $\alpha$-particle is: $^4_2 He$ On emission: $^A_Z X \rightarrow ^{A-4}_{Z-2} Y + ^4_2 He$

• mass number decreases by $4$
• atomic number decreases by $2$

Since $Z$ changes, the product is a different element.

So, C is incorrect.

(D) $\beta$-particle emission

In $\beta^-$ emission: $^A_Z X \rightarrow ^A_{Z+1} Y + ^0_{-1} e$

• mass number remains the same
• atomic number increases by $1$

Since $Z$ changes, the product is a different element.

So, D is incorrect.

Conclusion

Only neutron emission keeps the atomic number unchanged and changes the mass number, thus generating an isotope.

Therefore, the correct option is: $\boxed{\text{A}}$

Comparison with stored answer

Stored correct answer: A

My derived answer: A

They agree.