A) \[\frac{2\,\nu }{A+4}\]
B) \[\frac{4\,\nu }{A+4}\]
C) \[\frac{4\,\nu }{A-4}\]
D) \[\frac{2\,\nu }{A-4}\]
Correct Answer: C
Solution :
\[\alpha -particle\] 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 \[_{Z}{{X}^{A}}{{\xrightarrow{\alpha -particle}}_{z-2}}{{X}^{A-4}}{{+}_{z}}H{{e}^{4}}\,(\alpha -Particle)\] Also from the law of conservation of momentum, \[\operatorname{m}\,\,\times \,\,0\,\,=\,\,{{m}_{y}}{{\nu }_{y}}\,\,+\,\,{{m}_{\alpha }}{{\nu }_{\alpha }}\] \[=\left( A-4 \right){{\nu }_{y}}+4\nu \] \[\Rightarrow \,\,\,\,\,\,{{\nu }_{y}}=\frac{4\nu }{A-4}\]
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