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A radioactive substance decays at a rate proportional to the amount of substance present. If half of the substance decays in 100 years, then what is the decay constant (proportionality constant)?

Options

  1. An 2 100
  2. Bn 5 100
  3. Cn 10 100
  4. D2 n 2 100

Correct answer

A. n 2 100

Step-by-step solution

aligned & dP dt =- kP & 1 p dp =- k dt aligned aligned & p =- kt + C & When =0, P =8 P & = C = & put t =100 and C = np & n ( p / 2)=-100 k + lnp & n - 2=-100 k = np & k = n 2 100 aligned

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