MATH SOLVE

7 months ago

Q:
# Technetium-99m, a radioisotope used to image the skeleton and the heart muscle, has a half-life of about 6 hours. Find the decay constant. Use the decay function N(t)=N0e−kt to determine the amount of a 250 mg dose that remains after 24 hours. 16 mg or 63 mg or 125 mg or 3998 mgplz show how to solve the equations

Accepted Solution

A:

The decay constant is i 0.1155, and there would be 16 mg left after 24 hours.

The relationship between the half-life, T₀.₅, and the decay constant, λ, is given by

T₀.₅ = 0.693/λ.

Solving for λ, we will multiply both sides by λ first:

(T₀.₅)(λ) = 0.693

Since we know the half life is 6 hours, this gives us:

6λ = 0.693

Dividing by 6, we have

λ = 0.693/6 = 0.1155.

The decay constant will be k in our decay formula, and N₀, the original amount of substance, is 250:

N(24) = 250e^(-0.1155*24) = 15.6 ≈ 16

The relationship between the half-life, T₀.₅, and the decay constant, λ, is given by

T₀.₅ = 0.693/λ.

Solving for λ, we will multiply both sides by λ first:

(T₀.₅)(λ) = 0.693

Since we know the half life is 6 hours, this gives us:

6λ = 0.693

Dividing by 6, we have

λ = 0.693/6 = 0.1155.

The decay constant will be k in our decay formula, and N₀, the original amount of substance, is 250:

N(24) = 250e^(-0.1155*24) = 15.6 ≈ 16