An element A undergoes successive radioactive decay following sequence $β^{-}, β^{-}, X, β^{-}, β^{-}, Y$ to form product B. Select incorrect statement.

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If Xis $α$ -particle and Y is $β$ -particle then A and B are isodiaphers

If X and Y both are positrons then A and B are isobars

If X and Yboth are $β$ -particles then A andB are isobars

If X and Y both are ' $α$ ' particles, then A and B are isotopes

answer is D.

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Detailed Solution

(a) $_{Z}^{M} A \overset{- 2 β^{- i}}{⟶} \underset{Z + 2}{M} A \overset{\underset{\to}{- α}}{X} \underset{Z}{M - 4} A \overset{- 2 β^{- 1}}{⟶} \underset{Z + 2}{M - 4} A \underset{Y}{⟶} \underset{Z}{M - 8} A (B)$

(b) $_{Z}^{M} A \overset{- 2 β^{-}}{⟶} \underset{z + 2}{M} A \overset{β^{+}}{X} \underset{z + 1}{M} A \overset{- 2 β^{-}}{⟶} \underset{z + 3}{M} A \underset{γ}{\overset{β^{+}}{⟶}} \underset{z + 2}{M} A (B)$

(c) $_{Z}^{M} A \overset{- 2 β^{-}}{⟶} \underset{Z + 2}{M} A \underset{X}{\overset{- β^{-}}{⟶}} \underset{z + 3}{M} A \overset{- 2 β^{-}}{⟶} \underset{z + 5}{M} A \underset{γ}{\overset{- β^{-}}{⟶}} \underset{z + 6}{M} A (B)$

(d) $_{Z}^{M} A \overset{- 2 β^{-}}{⟶} \underset{Z + 2}{M} A \underset{X}{\overset{- α}{⟶}}_{Z}^{M - 4} A \overset{- 2 β^{-}}{⟶} \underset{Z + 2}{M - 4} A \underset{γ}{\overset{- β^{-}}{⟶}} \underset{Z + 3}{M - 4} A (B)$