How many alpha and beta particles are emitted when Uranium $_{92} \mathrm{U}^{238}$ decays to lead $_{82} \mathrm{~Pb}^{206}$ ?

(D) 8 alpha particles and 6 beta particles

(A) 3 alpha particles and 5 beta particles

(B) 6 alpha particles and 4 beta particles

(C) 4 alpha particles and 5 beta particles

JEE Main · 2022 · 26 Jun 2022 · Shift 1 · Modern Physics

How many alpha and beta particles are emitted when Uranium

_{92} U^{238}

decays to lead

_{82} Pb^{206}

(A)3 alpha particles and 5 beta particles
(B)6 alpha particles and 4 beta particles
(C)4 alpha particles and 5 beta particles
(D)8 alpha particles and 6 beta particles✓ Correct

Answer: (D)

Solution

Each alpha decay reduces mass number by 4 and atomic number by 2. Each beta decay increases atomic number by 1 without changing mass number. Mass change:

238 - 206 = 32 = 8 \times 4

, so 8 alpha particles are emitted. Atomic number change from alpha alone:

92 - 8 \times 2 = 76

. To reach

Z = 82

, we need

82 - 76 = 6

beta decays. The decay is:

_{92}^{238} U \to 8_{2}^{4} He + 6_{- 1}^{0} e +_{82}^{206} Pb

JEE Main · 2022 · 26 Jun 2022 · Shift 1 · Single correct option

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