A shaker of salt substitute contains 1.6 oz of K. What is the activity,

¿A shaker of salt substitute contains 1.6 oz of K. What is the activity, in milliCuries, of the potassium in the shaker? The activity is 7 microcuries (µCi)

2 months ago

Solution 1

Guest Guest #3859
2 months ago
We know K-40 (potassium having atomic mass 40 g) is radioactive and its natural abundance is 0.012% 
So for 1 mol of potassium contains 0.00012 mol of K-40 
Now 1.6 oz of K = 45.36 g of K
average atomic weight of K = 39.1 g
so 45.36 g of K contains:
(45.36 / 39.1) * 0.00012 * 6.022 x 10²³ (atoms of K-40)
= 8.4 x 10¹⁹ atoms of K-40
We know, activity A is:
A = 0.693 / t1/2 N₀
[t1/2 : half life time and N₀ : initial number of atoms]
t1/2 of K-40 = 1.28 x 10⁹ years
    = 4.04 x 10¹⁶ seconds
So A = (0.693 / 4.04 x 10¹⁶) * (8.4 x 10¹⁹ ) = 1441 cps
A = 141 x (1/3.7 x 10¹⁰)   because 3.7 x 10¹⁰ cps = 1 Ci
A = 3.9 x 10⁻⁸ Ci  = 3.9 x 10⁻⁵ millicurie

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