The specific activity of a sample of sodium, containing only Na23 and Na24, is 1.25 × 1015 disintegrations per second per gram. The mass percent of Na24 in the sample is : [Given : ln2 = 0.7, NA = 6.0×1023, t1/2 of Na24 = 14 hrs.]

Engineering

Chemistry

Kinetics of Radioactive Decay

Question

The specific activity of a sample of sodium, containing only Na²³ and Na²⁴, is 1.25 × 10¹⁵ disintegrations per second per gram. The mass percent of Na²⁴ in the sample is :

[Given : ln2 = 0.7, N_A = 6.0×10²³, t_1/2 of Na²⁴ = 14 hrs.]

36%

0.36%

3.6%

0.036%

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A = λN $λ = \frac{0 .693}{14 \times 60 \times 60} \sec^{- 1}$
Let the weight of Na²⁴ be xg in 1g of sample
1.25 × 10¹⁵ = $\frac{0 .693}{14 \times 60 \times 60} \times \frac{x}{24} \times 6 \times 10^{23}$
x = 3.6 × 10^–3
% of Na²⁴ = $\frac{3 .6 \times 10^{- 3}}{1} \times 100$ = 0.36 %