Identify the missing entries in the following nuclear reaction.

$${}_{11}^{22}{\rm{Na}} \to {}_ \ldots ^{22}{\rm{Ne}} + {}_ \ldots ^0e + {}_0^0 \ldots$$

Define half-life.

Sodium-22 has a decay constant of 0.27 yr^–1.

(i) Calculate, in years, the half-life of sodium-22.

(ii) A sample of sodium-22 has initially 5.0 × 10²³ atoms. Calculate the number of sodium-22 atoms remaining in the sample after 5.0 years.

${}_{11}^{22}{\rm{Na}} \to {}_{10}^{22}{\rm{Ne}} + {}_{ + 1}^0e + {}_0^0v$
${}_{10}^{22}{\rm{Ne}}$;
${}_{ + 1}^0e$ (accept ${}_ + ^0e$)
${}_0^0v$; (award [0] for ${}_0^0\bar v$)

time taken for half/50% of the nuclei to decay / activity to drop by half/50%;

(i) ${T_{\frac{1}{2}}} = \frac{{\ln 2}}{\lambda }$;
$\frac{{0.693}}{{0.27{\rm{y}}{{\rm{r}}^{ - 1}}}}$=2.6 (years);
Award [2] for a bald correct answer.

(ii) N=5.0 x 10²³ x e^-0.27x5.0;
N=1.3 x 10^23;
Award [2] for a bald correct answer.