13.12 Find the Q-value and the kinetic energy of the emitted α -particle in the α -decay of (a) Ra88226 and (b) Rn86220 . Given m ( Ra88226) = 226.02540 u, m ( Rn86222) = 222.01750 u, m ( Rn86222) = 220.01137 u, m ( Po)84216 = 216.00189 u.

13.12 α- particle decay of Ra88226 emits a helium nucleus. As a result, its mass number reduces to (226-4) 222 and its atomic number reduces to (88-2) 86. Ra88226 → Rn86222 + He24 Q value of emitted α- particle = (Sum of initial mass – Sum of final mass) *c2 , where c = Speed of light. It is given that m ( Ra88226) = 226.02540 u m ( Rn86222) = 222.01750 u m ( He24) = 4.002603 u Q value = [(226.02540) – (222.01750 + 4.002603)] c2 = 5.297 *10-3uc2 But 1 u = 931.5 MeV/ c2 Hence Q = 4.934 MeV Kinetic energy of the α- particle = MassnumberafterdecayMassnumberbeforedecay *Q = 222226 * 4.934= 4.85 MeV α- particle decay of Rn86220 emits a helium nucleus. As a result, its mass number reduces to (220-4) 216 and its atomic number reduces to (86-2) 84. Rn86220 → Po84216 + He24 Q value of emitted α- particle = (Sum of initial mass – Sum of final mass) *c2 , where c = Speed of light. It is given that m ( Rn86222) = 220.01137 u m ( Po)84216 = 216.00189 u m ( He24) = 4.002603 u Q value = [(220.01137) – (216.00189 + 4.002603)] c2 = 6.877 *10-3uc2 But 1 u = 931.5 MeV/ c2 Hence Q = 6.406 MeV Kinetic energy of the α- particle = MassnumberafterdecayMassnumberbeforedecay *Q = 216222 * 6.406= 6.23 MeV

13.12 Find the Q-value and the kinetic energy of the emitted $α$ -particle in the $α$ -decay of (a) ${}_{88}^{226}{R a}$ and (b) ${}_{86}^{220}{R n}$ . Given m ( ${}_{88}^{226}{R a})$ = 226.02540 u, m ( ${}_{86}^{222}{R n})$ = 222.01750 u, m ( ${}_{86}^{222}{R n})$ = 220.01137 u, m ( ${}_{84}^{216}{P o)}$ = 216.00189 u.

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Payal Gupta | Contributor-Level 10

7 months ago

13.12 $α -$ particle decay of ${}_{88}^{226}{R a}$ emits a helium nucleus. As a result, its mass number reduces to (226-4) 222 and its atomic number reduces to (88-2) 86.

${}_{88}^{226}{R a}$ $\to$ ${}_{86}^{222}{R n}$ + ${}_{2}^{4}{H e}$