Sodium-23 (in a sample of NaCl) is subjected to neutron bombardment in a nuclear reactor to produce ²⁴Na. When removed from the reactor, the sample is radioactive, with β activity of 2.54 × 10⁴ dpm. The decrease in radioactivity over time was studied, producing the following data:

(a) Write equations for the neutron capture reaction and for the reaction in which the product of this reaction decays by β emission.
(b) Determine the half-life of sodium-24.

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Activity (dpm) Time (hours) 2.54 x 104 0 2.42 x 104 1 2.31 x 104 2 5 2.00 x 104 1.60 x 104 1.01 x 104 10 20