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Barium-142 is used as a GI radiocontrast agent. After 1.25 hours, 9.25 μg remains in the patient. Determine the original dose given the half-life of Ba-142 is 10.6 minutes. 

The answer is about 1184 or 1180

Verified Answer :

SenpaiTrill

hello there.

Barium-142 is used as a GI radiocontrast agent. After 1.25 hours, 9.25 μg remains in the patient. Determine the original dose given the half-life of Ba-142 is 10.6 minutes. 

1180

Dejanras

Answer is: the original dose is 1180 μg.

m₀(Ba-142) = ?; initial mass of Ba-142.

m(Ba-142) = 9.25 μg; mass of  remaining at time.

t = 10.6 min.; half-life of Ba-142.

t₁ = 1.25 h · 60 min/h.

t₁ = 75 min.

First calculate the radioactive decay rate constant λ:

λ = 0.693 ÷ t.

λ  = 0.693 ÷ 10.6 min.

λ  = 0.0654 1/min.

ln(m/m₀) = -λ·t₁.

ln(9.25μg/m₀) = -0.0654 1/min · 75 min.

ln(9.25μg/m₀) = -4.90.

m₀ = 1180 μg.

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