Read the information given below to answer
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 \( Q = \Delta m \cdot c^{2} \)
An \( \alpha \)-decay process is given by
\( {}^{A}_{Z}X \longrightarrow {}^{A-4}_{Z-2}Y + {}^{4}_{2}\mathrm{He} \)
If mass of nuclei \( X \), \( Y \) and He are \( m_x \), \( m_y \) and \( m_{\mathrm{He}} \) respectively, then \( Q \)-value is given by
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → \( (m_x - m_y - m_{\mathrm{He}})c^{2} \)
The Q-value is the energy released, equal to the mass defect (mass before the decay minus mass after it) times \( c^2 \), from Einstein's mass-energy relation.
\( \text{Mass before} = m_x \)
\( \text{Mass after} = m_y + m_{\mathrm{He}} \)
\( \displaystyle Q = \left[m_x - (m_y + m_{\mathrm{He}})\right]c^{2} = (m_x - m_y - m_{\mathrm{He}})c^{2} \)
For a spontaneous decay this is positive, because the products are lighter than the parent.
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 difference between the initial mass energy and the final mass energy of the decay products is called the Q value of the process or the disintegration energy. Thus, the Q value of an alpha decay can be expressed as
\( \displaystyle Q = (m_X - m_Y - m_{He})\,c^{2} \qquad (13.21) \)”