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haeologists include sandals from a cave in oregon. the carbon in the sandals is observed to undergo beta decay at a rate of 5.1 disintegrations per minute per gram of carbon. the carbon in living organisms decays at a rate of 15 disintegrations per minute per gram of carbon. calculate the age of the sandals, given that the half-life of carbon-14 is 5730 years.

Respuesta :

The age of the sandals, given that the half-life of carbon-14 is 5730 years is 8900 years old.

Half-lifestyles is usually defined as the time wished by a radioactive substance (or one half the atoms) to fall apart or transform into a exceptional substance. The precept changed into first observed in 1907 with the aid of Ernest Rutherford. additionally it is represented through the image Ug or t1/2.

Calculation:-

¹⁴C/¹²C = 1.3 × 10⁻²

decay rate = 15 dpm/gC

half life = 5730

disintegration per min = 5.1 dpm

ln N/N₀ = -kt

A₀/A = kN₀/kN = N₀/N

A₀/A = 15/5.1

    t₁/₂ = 0.693/K

   K = 0.693/t₁/₂

       = 0.693 /5730 yrs

      = 1.21 × 10⁻⁴ yrs ⁻¹

t = ln(N₀/N)/K = ln(15/5.1)/1.21 × 10⁻⁴ yrs ⁻¹

t = 8900 years old.

 

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