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NEET-XII-Physics

46: The Nucleus

with Solutions - page 6
Qstn# iv-21 Prvs-QstnNext-Qstn
  • #21
    Radioactive 131I has a half-life of 8.0 days. A sample containing 131I has activity 20 µCi at t = 0. (a) What is its activity at t = 4 days? (b) What is its decay constant at t = 4.0 days?
    Ans : Given:
    Half-life of radioactive 131I, T1/2 = 8 days
    Activity of the sample at t = 0, A0 = 20 µCi
    Time, t = 4 days (a) Disintegration constant, `` \lambda =\frac{0.693}{{T}_{1/2}}=0.0866``
    Activity (A) at t = 4 days is given by
    `` A={A}_{0}{e}^{-\lambda t}``
    `` \Rightarrow A=20\times {10}^{-6}\times {e}^{-0.0866\times 4}``
    `` =1.41\times {10}^{-6}\,\mathrm{\,Ci\,}=14\,\mathrm{\,\mu Ci\,}`` (b) Decay constant is a constant for a radioactive sample and depends only on its half-life.
    `` \lambda =\frac{0.693}{[8\times 24\times 3600]}``
    `` =1.0026\times {10}^{-6}{\,\mathrm{\,s\,}}^{-1}``
    Page No 443:
  • #21-a
    What is its activity at t = 4 days?
    Ans : Disintegration constant, `` \lambda =\frac{0.693}{{T}_{1/2}}=0.0866``
    Activity (A) at t = 4 days is given by
    `` A={A}_{0}{e}^{-\lambda t}``
    `` \Rightarrow A=20\times {10}^{-6}\times {e}^{-0.0866\times 4}``
    `` =1.41\times {10}^{-6}\,\mathrm{\,Ci\,}=14\,\mathrm{\,\mu Ci\,}``
  • #21-b
    What is its decay constant at t = 4.0 days?
    Ans : Decay constant is a constant for a radioactive sample and depends only on its half-life.
    `` \lambda =\frac{0.693}{[8\times 24\times 3600]}``
    `` =1.0026\times {10}^{-6}{\,\mathrm{\,s\,}}^{-1}``
    Page No 443: