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 \( Q = \Delta m \cdot c^{2} \)
\( A \stackrel{\alpha}{\longrightarrow} B \stackrel{\beta}{\longrightarrow} C \stackrel{\beta}{\longrightarrow} D \)
In the process \( A \rightarrow B \), \( \alpha \) particle is emitted by nucleus and in process \( B \rightarrow C \) and \( C \rightarrow D \) each, one – \( \beta \) – particle is emitted.
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → B, C, D are Isobars
Alpha decay lowers the mass number by 4 and the atomic number by 2. Beta-minus decay keeps the mass number the same and raises the atomic number by 1. Let A be \( {}^{M}_{Z}A \).
\( A: \ (M,\ Z) \)
\( B: \ (M-4,\ Z-2) \)
\( C: \ (M-4,\ Z-1) \)
\( D: \ (M-4,\ Z) \)
Isobars have the same mass number; isotopes have the same atomic number.
Option (1) A, B, C are Isotopes — Incorrect. The atomic numbers of A, B and C are \( Z, Z-2, Z-1 \), all different, so they are not isotopes.
Option (2) B, C, D are Isobars — Correct. B, C and D all have mass number \( M - 4 \), so they are isobars.
Option (3) A, B, C are Isobars — Incorrect. A has mass number \( M \) while B and C have \( M - 4 \), so the three are not isobars.
Option (4) A, B, C, D all are Isotopes — Incorrect. The atomic numbers are \( Z, Z-2, Z-1, Z \); only A and D share an atomic number (they are isotopes of each other), not all four.
Note: The definition of isobars used in this question is from the latest textbook (2026-27). How alpha decay and beta decay change the mass number is printed only in the pre-rationalised textbook (2022-23). It was removed from the latest book, and it also appears to be out of the CUET 2026 syllabus.
NCERT (2026-27):
Atomic Masses and Composition of Nucleus – “… All nuclides with same mass number A are called isobars. For example, the nuclides 31H and 32He are isobars.”
NCERT (Pre-rationalised edition, 2022-23):
Alpha Decay – “… In this process, it is observed that since 42He contains two protons and two neutrons, the mass number and the atomic number of the daughter nucleus decreases by four and two, respectively.”
Beta Decay – “… These processes show why the mass number A of a nuclide undergoing beta decay does not change; one of its constituent nucleons simply changes its character according to Eq. (13.24) or (13.25).”