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In α-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, α-decay of parent nucleus +2^He

\({ }_Z^A X \) results in daughter nucleus \({ }_{Z-2}^{A-4} Y\)

\({ }_Z^A X \longrightarrow{ }_{Z-2}^{A-4} Y+2^{\mathrm{He}^4} \)

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 products. By referring the table of nuclear masses, one can check that the total mass of daughter nucleus and α-particle is indeed less than that of parent nucleus.

The disintegration energy or the Q value can be calculated by formula Q = Δm.c²

An α-decay process is given by

\( { }_Z^A X \longrightarrow{ }_{Z-2}^{A-4} Y + { }_2^4 He \)

If mass of nuclei X, Y and He are m_x, m_y and m_He respectively, then Q-value is given by

(m_x – m_y – m_He)c²

Q value = difference of mass energy of Parent and daughter nucleus = mass energy of [Initial nuclei – Final product nucleus]

∴ Mass energy = Δmc²

∴ Q = [m_x – (m_y + m_He)]c²