Symbol D
D is part of the quantity the equation computes from the expression on the right.
Read this term in its guide →Published equation contexts
Why this formula appears here
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 . 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.
Read the representative guide
Symbol N
N occurs below the fraction bar. The quantity above the bar is divided by this expression; zero is excluded as a denominator.
Read this term in its guide →Symbol pi
pi occurs below the fraction bar. The quantity above the bar is divided by this expression; zero is excluded as a denominator.
Read this term in its guide →Symbol k
k occurs below the fraction bar. The quantity above the bar is divided by this expression; zero is excluded as a denominator.
Read this term in its guide →Denominator: 6pi k P
The complete quantity below the fraction bar; it must be nonzero for this division.
Read this term in its guide →How to interpret it
With a fixed numerator, increasing a nonzero denominator reduces the fraction. Read it with the definitions, units, and assumptions supplied by the article.
Research cited beside this formula
Published contexts (1)
A symbol can carry a different meaning in another article. Each occurrence keeps its own guide and term definitions.
Equation 7 · Einstein & Evolution
Einstein's Random Walk and the Mathematics of Genetic Drift
This equation states an equality: the expressions on both sides have the same value under the article’s assumptions.
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 . 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.