Answer:
t₁/₂ = 45.1 min
Explanation:
The radioactive decay equation is given by
N/N₀ = e^-kt where N = counts after time t
N₀ = counts initially
k = decay constant
t= time elapsed
The question is what´s the half-life of this substance, and we can solve it once we have k from the expression above since
t₁/₂ = 0.693/k
which is derived from that equation, but for the case N/N₀ is 0.5
Lets calculate k and t₁/₂ :
N/N₀ = e^-kt (taking ln in the two sides of the equation)
ln (N/N₀) = ln e^-kt = -kt ⇒ k = -ln(N/N₀)/t
k = -ln(100/400)/90.3 min = 0.01535 min⁻¹
t₁/₂ = 0.693/k = 0.693/0.01535 min⁻¹ = 45.1 min
We can check this answer since the time in the question is the double of this half-life and the data shows the material has decayed by a fourth: two half-lives.
