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Question

Question: If \(92U^{238}\) undergoes successively 8 α-decays and 6 β-decays, then resulting nucleus is....

If 92U23892U^{238} undergoes successively 8 α-decays and 6 β-decays, then resulting nucleus is.

A

82U20682U^{206}

B

82Pb20682Pb^{206}

C

82U21082U^{210}

D

82U21482U^{214}

Answer

82Pb20682Pb^{206}

Explanation

Solution

(Z=92)U(A=238)(8α,6β)ZXA(Z = 92)U^{(A = 238)}{\overset{\quad(8\alpha,6\beta)\quad}{\rightarrow}}_{Z^{'}} ⥂ X^{A^{'}}

So A=A4nαA^{'} = A - 4n_{\alpha}= 238 – 4 × 8 = 206

and Z=nβ2nα+zZ^{'} = n_{\beta} - 2n_{\alpha} + z = 6 – 2 × 8 + 92 = 82.