KVPY Sample Paper KVPY Stream-SX Model Paper-22

In a decay series, \[_{82}^{206}Pb\] is obtained at the end from \[_{92}^{238}U.\] How many alpha and beta particles must have been emitted?

A) \[7\alpha ,10\beta \]

B) \[8\alpha ,6\beta \]

C) \[5\alpha ,6\beta \]

D) \[6\alpha ,8\beta \]

Correct Answer: B

Solution :

\[\underset{92}{\mathop{238}}\,U\to \underset{82}{\mathop{206}}\,Pb\]

Number of \[\alpha \]-particles

\[=\frac{chnages\,\,in\,\,mass\,\,number}{4}\]

\[=\frac{238-206}{4}\]

\[=\frac{38}{4}=8\alpha \]

Number of \[\beta \]-particles \[=2\times \] number of \[\alpha \]-particles - change in atomic number

\[=2\times 8-\left( 92-82 \right)\]

\[=16-10=6\beta \]