A sample of radium-226 will decay to ¼ of its original amount after 3200 years. What is the half-life of radium-226? years

t(half-life) = 1600 yrs

Explanation:

All radio decay follows 1st order kinetics and therefore can be applied to the expression A = A₀e^(-kt)

A = current activity

A₀ = initial activity

k = decay constant

t = time of decay

Half-Life = 0.693/k

k = ln(A/A₀) / -t = ln(0.25) / -3200yrs = 4.33x 10⁻⁴ yrs⁻¹

Half-Life => t(1/2) = (0.693/4.33 x 10⁻⁴)yrs⁻¹ = 1600 yrs.

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