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In \( \alpha \)-decay, the mass number of daughter nucleus is four less than that of decaying nucleus (parent nucleus). While atomic number decreases by two. In general, \( \alpha \)-decay of parent nucleus \( {}^{A}_{Z}X \) results in daughter nucleus \( {}^{A-4}_{Z-2}Y \)
\( {}^{A}_{Z}X \longrightarrow {}^{A-4}_{Z-2}Y + {}^{4}_{2}\mathrm{He} \)
From Einstein’s mass energy equivalence relation and energy conservation, it is clear that this spontaneous decay is possible only when mass of decay products is less than the mass of the parent nucleus. By referring the table of nuclear masses, one can check that the total mass of daughter nucleus and \( \alpha \)-particle is indeed less than that of parent nucleus.
The disintegration energy or the \( Q \) value can be calculated by formula \( Q = \Delta m \cdot c^{2} \)
During the \( \alpha \)-decay process, the mass of all decay product is
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → Less than the mass of initial nucleus
A decay happens on its own only if it releases energy, that is, only if \( Q \gt 0 \). By energy conservation this energy comes from mass that disappears.
\( \displaystyle Q = \left[m_{\mathrm{parent}} - (m_{\mathrm{daughter}} + m_{\alpha})\right]c^{2} \gt 0 \)
\( m_{\mathrm{daughter}} + m_{\alpha} \lt m_{\mathrm{parent}} \)
So the total mass of the decay products is less than the mass of the initial nucleus; the difference appears mainly as the kinetic energy of the \( \alpha \)-particle and the daughter nucleus.
Note: This question is from the pre-rationalised NCERT book (2022-23). The topic was removed from the latest NCERT book (2026-27), and it also appears to be out of the CUET 2026 syllabus.
NCERT (Pre-rationalised edition, 2022-23):
Alpha Decay – “… The alpha-decay of 23892U can occur spontaneously (without an external source of energy) because the total mass of the decay products 23490Th and 42He is less than the mass of the original 23892U.”