List-I shows different radioactive decay processes and List-II provides possible emitted particles. Match each entry in List-I with an appropriate entry from List-II, and choose the correct option. [2023]

Question

List-I shows different radioactive decay processes and List-II provides possible emitted particles. Match each entry in List-I with an appropriate entry from List-II, and choose the correct option. [2023]

	List-I		List-II
(P)	${}_{92}^{238}U \to {}_{91}^{234}{Pa}$	(1)	one $α$ particle and one $β^{+}$ particle
(Q)	${}_{82}^{214}{Pb} \to {}_{82}^{210}{Pb}$	(2)	three $β^{-}$ particles and one $α$ particle
(R)	${}_{81}^{210}{Tl} \to {}_{82}^{206}{Pb}$	(3)	two $β^{-}$ particles and one $α$ particle
(S)	${}_{91}^{228}{Pa} \to {}_{88}^{224}{Ra}$	(4)	one $α$ particle and one $β^{-}$ particle
		(5)	one $α$ particle and two $β^{+}$ particles

Smart Achievers · Accepted Answer

(1)

In $α$ -decay, mass number (A) decreases by 4 units and atomic number (Z) decreases by 2 units.

In $β^{-}$ decay, A does not change but Z increases by 1 unit.

In $β^{+}$ decay, A does not change but Z decreases by 1 unit.

(P) ${}_{92}U^{238} \to {}_{91}{Pa}^{234}$

$β^{+}$

$N_{2} - N_{3} = (92 - 91) - \frac{4}{2} = - 1 \to 1 β^{-}$

$∴$ $1 α and 1 β^{-} emission.$

(Q) ${}_{82}{Pb}^{214} \to {}_{82}{Pb}^{210}$

$N_{1} = \frac{214 - 210}{4} = 1 \to 1 α$

$N_{2} - N_{3} = (82 - 82) - \frac{4}{2} = - 2 \to 2 β^{-}$

$∴$ $1 α and 2 β^{-} emission.$

(R) ${}_{81}{Tl}^{210} \to {}_{82}{Pb}^{206}$

$N_{1} = \frac{210 - 206}{4} = 1 \to 1 α$

$N_{2} - N_{3} = (81 - 82) - \frac{4}{2} = - 3 \to 3 β^{-}$

$∴$ $1 α and 3 β^{-} emission.$

(S) ${}_{91}{Pa}^{228} \to {}_{88}{Ra}^{224}$

$N_{1} = \frac{228 - 224}{4} = 1 \to 1 α$

$N_{2} - N_{3} = (91 - 88) - \frac{4}{2} = 1 \to 1 β^{+}$

$∴$ $1 α and 1 β^{+} emission.$

Solution

1 P → 4, Q → 3, R → 2, S → 1

2 P → 4, Q → 1, R → 2, S → 5

3 P → 5, Q → 3, R → 1, S → 4

4 P → 5, Q → 1, R → 3, S → 2

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