A nucleus of ${ }_{84}^{210} \mathrm{Po}$ originally at rest emits $\alpha$ particle with speed v. What will be the recoil speed of the daughter nucleus
Answer & explanation
Correct answer: option 1
${ }_{84} \mathrm{Po}^{210} \rightarrow{ }_{82} X^{206}+{ }_2 \mathrm{He}^4$
Using conservation of linear moments
$206 v'+4 v=0 \Rightarrow v'=-\frac{4 v}{(206)} \Rightarrow\left|v'\right|=\frac{4 v}{206}$