Number of particles emitted in the nuclear reaction, 88 Ra 224 ⟶ 82 Ra 208 are

Question

Number of particles emitted in the nuclear reaction, 88 ​ Ra 224 ⟶ 82 ​ Ra 208 are

TestHub · Accepted Answer

Alpha decay reduces mass number by 4, atomic number by 2. Beta decay increases atomic number by 1.

For $_{88}^{224} R a ⟶_{82}^{208} R a$ :

Mass change: $224 - 208 = 16$ . Number of $α$ particles = $16/4 = 4$ .

Atomic number change from $α$ decay: $4 \times 2 = 8$ .

Expected atomic number after $4 α$ decays: $88 - 8 = 80$ .

Actual final atomic number: $82$ .

Difference: $82 - 80 = 2$ . This means 2 $β$ particles were emitted.

So, $(4 α, 2 β)$ particles are emitted.

Concepts: Alpha decay ( $_{2}^{4} He$ ), Beta decay ( $_{- 1}^{0} e$ ). Conservation of mass and atomic numbers.

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