a sample of 32 grams of unknown substances has a half life of 12 years. write an equation to determine the amount of substances (s) left after year T
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Answer:
Nt = 32e^(-0.05775 t)
Step-by-step explanation:
ln (Nt/N₀) = -kt
Nt = mass of radioactive material at time interval (t)
N₀ = mass of the original amount of radioactive material
k = decay constant
t = time interval (t1/2 for the half-life)
ln (Nt/N₀) = -kt
N₁₂ = 16 gram
N₀ = 32 gram
t = 12
ln(1/2) = -12k
-0.693 = -12k
=> k = 0.05775
ln (Nt/N₀) = -0.05775 t
ln (Nt/32) = -0.05775 t
Nt/32 = e^(-0.05775 t)
=>Nt = 32e^(-0.05775 t)
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