 Solution

ID: past-exam-of-the-physics-a-course-of-the-university-of-cambridge/2021/paper-1/section-c/c8/a/solution

Take the natural logarithm of the exponential decay model. To keep the logarithm dimensionless, choose the reference rate

R_{*} = 1 count da y^{- 1}

x = t, y = ln (R / R_{*}), m = - \frac{1}{τ}, c = ln (R_{0} / R_{*}) .

Then

y = m x + c

. With time measured in picoseconds, the slope has units

ps^{- 1}

and the intercept is dimensionless. A straight-line linear regression in these variables therefore estimates the inverse mean lifetime and logarithmic normalization.

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