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Equation 7 · Part 13 · Einstein's Random Walk and the Mathematics of Genetic Drift

Denominator: 6pi k P

D=RTN⋅16πkP,D = \frac{RT}{N}\cdot\frac{1}{6\pi k P},
6πkP6\pi k P

What this part means

The complete quantity below the fraction bar; it must be nonzero for this division.

Its job in the formula

6pi k P occurs below the fraction bar. The quantity above the bar is divided by this expression; zero is excluded as a denominator.

The passage around this formula

with the diffusion constant D fixed by measurable quantities. Einstein derived it explicitly, from the balance between the drag on a sphere of radius P in a fluid of viscosity k and the osmotic pressure driving diffusion, as D=RTN⋅16πkPD = \frac{RT}{N}\cdot\frac{1}{6\pi k P}. where R is the gas constant, T the absolute temperature, and N Avogadro’s number [ 1 ] . That last dependency was the trap door: if D could be read off a microscope by timing how far a particle wandered, and every other term in the equation was already known independently, then watching one particle jiggle became a way to count atoms.

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Learn the underlying idea

A fraction a/b means a divided by b. The top number is the numerator; the bottom number is the denominator, and it cannot be zero.

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Sources cited in the surrounding passage

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