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Concepts Of Physics MCQ Edition [Volume 2]PhysicsThe Nucleus

For a radioactive sample containing ¹²⁸ I , let R₀ be the initial count rate and R be the count rate of the nuclear radiation at time t . What is the nature of the plot of (R₀/R) against t ? Time t (minute) 0 25 50 75 100 Count rate R ( 10⁹ s ⁻¹ ) 30 16 8.0 3.8 2.0

Options

  1. AA parabola passing through the origin
  2. BA straight line passing through the origin
  3. CA straight line with a non-zero y-intercept
  4. DAn exponential curve

Correct answer

B. A straight line passing through the origin

Step-by-step solution

According to the law of radioactive decay, the count rate R at time t is given by: R = R₀ e^ - t where R₀ is the initial count rate and is the decay constant. Rearranging the equation, we get: R₀ R = e^ t Taking the natural logarithm on both sides: ( R₀ R ) = t Comparing this with the equation of a straight line y = mx + c , we have y = (R₀/R) , x = t , m = , and c = 0 . Thus, the plot of (R₀/R) against t is a straight line passing through the origin.

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