Final answer:
The half-life of the radioactive material can be calculated using the decay constant and the relationship t₁/₂ = 0.693 / λ. With a given decay rate of -10-9s-1, the half-life is found to be approximately 22 years.
Step-by-step explanation:
To calculate the half-life of a radioactive element when given a decay rate (the slope value from a ln(A) versus t plot), you can use the relationship between the decay constant (λ) and half-life (t₁/₂). This relationship is given by the formula t₁/₂ = 0.693 / λ. With the provided decay rate of -10-9s-1, the half-life can be calculated as follows:
t₁/₂ = 0.693 / (-10-9s-1)
Plugging in the decay rate value, we get:
t₁/₂ = 0.693 / (10-9s-1)
Hence:
t₁/₂ = 693,000,000 seconds
To convert seconds to years, divide by the number of seconds in a year (approximately 31,536,000).
t₁/₂ ≈ 22 years (rounded to two significant figures)
Therefore, the half-life of the radioactive material is approximately 22 years.