Question

Find the Q-value and the kinetic energy of the emitted $\alpha$- Particle in the $\alpha$-decay of (a) ${}_{86}^{220}Rn$ and (b) ${}_{88}^{226}Ra$.

Given:
$m{(}_{88}^{226}Ra)=226.02540u$,
$m{(}_{86}^{222}Rn)=222.01750u$,
$m{(}_{84}^{216}Po)=216.00189u$

Answer 1

(a)

${}_{88}^{226}Ra{\to }_{86}^{222}Rn{+}_2^4\alpha$

${}_{86}^{222}Rn{\to }_{84}^{216}Po{+}_2^4\alpha$

$Q=\Delta m\times 931MeV$

$\Delta m=226.02540-222.01750-4.002603=0.005297$

Q = 4.93 MeV,

$E_{\alpha }=4.85MeV$

Kinetic energy $=\frac{Massno.afterdecay}{Massno.beforedecay}\times Q$

$K.E=\frac{222}{226}\times 4.93=4.85MeV$

(b) ${}_{86}^{222}Rn{\to }_{84}^{216}Po{+}_2^4\alpha$

$Q=\Delta m\times 931MeV$

$\Delta m=220.01137-216.00189-4.002603=0.006877$

Q = 6.4 MeV,

$E_{\alpha }=6.29MeV$

Kinetic energy $=\frac{Massno.afterdecay}{Massno.beforedecay}\times Q$

$K.E=\frac{216}{222}\times 6.4=6.29MeV$