lals asked in Science & MathematicsPhysics ยท 1 month ago

maths: differencial ย equations?

The rate at which a radioactive specimen decays is given by

d๐‘/d๐‘ก=โˆ’๐›ผ๐‘

where ๐‘ is the number of radioactive particles at time ๐‘ก and ๐›ผ is a constant. Solve this equation to find an expression for ๐‘ as a function of time given that ๐‘=๐‘0 at ๐‘ก=0. Hence find the half-life of the specimen i.e. the time taken for the number of radioactive particles to halve.

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  • 1 month ago

    dN/N = -alpha dt =>

    N = c e^(-alpha t),

    and N(0) = No implies

    N = No * e^(-alpha t).

    The half-life is the time when

    1/2 = e^(-alpha t), or

    ln(2) = alpha t, or

    t = [ln(2)]/alpha.

  • The answer is as follows:

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