Calculate the mass of sodium chloride:

Problem:

Let us calculate the mass of sodium chloride in a solution containing ²⁴Na (half-life, 15 h) whose activity is 5.7 mCi.

Suppose w be the weight of ²⁴Na present in sodium chloride

Answer:

We know that λ = 0.693/t_{1/ 2} = 0.693/15 × 60 × 60s^-1

Rate of disintegration - dN/dt = λ N = (0.693 /15 × 3600) × (m × 6.02 × 10²³/24)

= 3.219 w×10¹⁷ disintegrations per sec

Given that

Activity  = -dN/dt = 5.7 × 3.7 × 10 ⁷ = 3.219 m × 10¹⁷

.^.. m = 6.55 ×10 ^-10 g. or 0.655 ng ²⁴Na in NaCl

.^.. mass. of ²⁴NaCl in solution  = 0.655 × 59.5 /24 = 1.62 ng

It may be noted that disintegration per sec. (dps) is frequent referred to as the activity of a radioactive sample and measured as counts per second (cps) or per min (cpm). These are related by ε × (dps) = cps where ε is the efficiency of the detection system. A more useful parameter is specific activity defined as the activity per unit mass of the sample. For most typical radio analytical experiments, only mCi or µCi amounts of radioactivity is used and these weigh insignificantly (ng or pg) small.