Radon gas $(\mathrm{Rn})$ is produced by the $\alpha$ decay of radium ${ }_{88}^{226} \mathrm{Ra}$. (a) How many neutrons and how many protons are present in the nucleus of the isotope of $\mathrm{Rn}$ produced by this decay? (b) In the air in an average size room in a student basement apartment in Ithaca, NY, there are about $10^{7}$ Rn nuclei. The Rn nucleus itself is radioactive; it too decays by emitting an $\alpha$ particle. The half-life of Rn is $3.8$ days. How many $\alpha$ particles per second are emitted by decaying Rn nuclei in the room?