Identify the wrong nuclear equation :

The correct answer is Option (2) → \( {}_{83}^{210}\mathrm{B} \rightarrow {}_{84}^{211}\mathrm{P_{0}} + e^{-} + \bar{\gamma} \)

Every nuclear equation must conserve the mass number (the upper numbers) and conserve the charge number (the lower numbers) on the two sides. An electron or positron has mass number 0 and charge number \( -1 \) or \( +1 \); the small neutral particle written after it has mass number 0 and charge 0.

The paper writes B for bismuth and \( \mathrm{P_{0}} \) for polonium; the neutral particle printed as \( \gamma \) (\( \bar{\gamma} \)) is the neutrino (antineutrino).

Option (1) \( {}_{6}^{11}\mathrm{C} \rightarrow {}_{5}^{11}\mathrm{B} + e^{+} + \gamma \) — A valid equation. Mass number \( 11 = 11 + 0 \); charge number \( 6 = 5 + 1 \). This is beta-plus decay.

Option (2) \( {}_{83}^{210}\mathrm{B} \rightarrow {}_{84}^{211}\mathrm{P_{0}} + e^{-} + \bar{\gamma} \) — The wrong equation. The charge number balances (\( 83 = 84 - 1 \)), but the mass number does not: \( 210 \ne 211 + 0 \). In beta-minus decay a neutron changes into a proton inside the nucleus, so the mass number stays the same; the product must be \( {}^{210}_{84}\mathrm{Po} \).

Option (3) \( {}_{94}^{242}\mathrm{Pu} \rightarrow {}_{92}^{238}\mathrm{U} + {}_{2}^{4}\mathrm{He} \) — A valid equation. Mass number \( 242 = 238 + 4 \); charge number \( 94 = 92 + 2 \). This is alpha decay.

Option (4) \( {}_{54}^{120}\mathrm{Xe} + e^{-} \rightarrow {}_{53}^{120}\mathrm{I} + \gamma \) — A valid equation. Mass number \( 120 + 0 = 120 \); charge number \( 54 - 1 = 53 \). This is electron capture.

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):
Beta Decay – “… In beta-minus decay, a neutron transforms into a proton within the nucleus according to

    \( \displaystyle n \rightarrow p + e^{-} + \bar{\nu} \qquad (13.24) \)

whereas in beta-plus decay, a proton transforms into neutron (inside the nucleus) via

    \( \displaystyle p \rightarrow n + e^{+} + \nu \qquad (13.25) \)

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).”