C

Step 1: In X-ray spectroscopy, Kα and Kβ refer to specific groups of X-ray emissions that are characteristic of an element.
Step 2: Kα represents the transition of an electron from the L shell (n=2) to the K shell (n=1), while Kβ corresponds to the transition from the M shell (n=3) to the K shell (n=1).
Step 3: Thus, Kα and Kβ indicate distinct emissions associated with transitions of electrons in an atom, clearly implying that they are α and β emissions respectively of the characteristic X-ray.
Conclusion: Hence, the correct answer is Option C: α, β-emissions respectively.