A) \[\frac{2v}{A+4}\]
B) \[\frac{4v}{A+4}\]
C) \[\frac{4v}{A-4}\]
D) \[\frac{2v}{A-4}\]
Correct Answer: C
Solution :
Key Idea: \[\alpha \]-particle is equivalent to helium nucleus. The emission of an \[\alpha \]-particle from the atom of an element reduces its atomic number by 2, and mass number by 4. Hence, the radioactive emission is as follows: \[_{z}{{X}^{4}}{{\xrightarrow{\alpha -particle}}_{z-2}}{{Y}^{A-4}}{{+}_{z}}H{{e}^{4}}\] (\[\alpha \]-parole) Also form law of conservation of momentum, \[m\times 0={{m}_{u}}{{v}_{y}}+{{m}_{\alpha }}{{v}_{\alpha }}\] \[=(A-4){{v}_{y}}+4v\] \[\Rightarrow \] \[{{v}_{y}}=-\frac{4v}{A-4}\] Note: Negative sign of velocity indicates that it recoils in the direction opposite to that of \[\alpha \]-particle.
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