Question

A nucleus of ${}_{84}P{o}^{210}$ originally at rest emit $\alpha$ particle with speed v. Recoil speed of the daughter nucleus is

• A. $\frac{v}{210}$
• B. $\frac{v}{84}$
• C. $\frac{4v}{206}$
• D. $\frac{3v}{214}$

Answer 1

The correct option is C $\frac{4v}{206}$

The reaction will be like this ${}_{84}P{o}^{210}{\to }_{82}P{b}^{206}{+}_{2}H{e}^4$

the mass of $\alpha$ particle is $4m$ where $m$ is mass of a nucleon. So the mass of daughter nuclei will be $206m$

the net momentum should be zero as the parent nuclei was at rest.

so if the speed of daughter nuclei is $V$ then $V\left(206m\right)+4m\left(v\right)=0$

Then $magnitude$ of $V$ will be $V=\frac{2v}{103}$