Question

What was the initial quantity of vanadium-49, which has a half-life of 330 days, if after 540 days there is a 1,750 g sample remaining?a.)5,440.42g b.)3,500g C.) 8,700g d.)2,863.63g e.)98g

Answer 1

(a) 5440.42 g

Explanation:

The amount remaining (Q) is given in terms of the initial amount (Q₀) by the exponential decay formula ...

Q = Q₀(1/2)^(t/330) . . . . . where t is in days

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The amount after 540 days is ...

1750 g = Q₀(1/2)^(540/330) = 0.321666Q₀

Q₀ = (1750 g)/(0.321666) ≈ 5440.42 g

The initial quantity was about 5440.42 grams.