Question

Radium ${}^{226}Ra$, spontaneously decays to radon with the emission of an $\alpha$ -particle and a $\gamma$ ray. If the speed of the particle upon emission from an initially stationary radium nucleus is $1.5\times {10}^{7}m/s$, what is the recoil speed of the resultant radon nucleus? Assume the momentum of ray is negligible compared to that of $\alpha$ particle.

• A. $2.0\times {10}^{5}m/s$
• B. $2.7\times {10}^{5}m/s$
• C. $3.5\times {10}^{5}m/s$
• D. $1.5\times {10}^{7}m/s$

Answer 1

The correct option is B $2.7\times {10}^{5}m/s$

Conservation of linear momentum requires:
$m_{radon}{v}_{radon}=m_{helium}{v}_{helium}$with helium identified as the alpha particle.

The nuclear masses can be approximated by their mass numbers $\left(222and4\right)$.

Thus, the recoil speed of the radon is $m\left(4/222\right)\times 1.5\times {10}^{7}m/s=2.7\times {10}^{5}m/s$.