You have just very gently exhaled a helium atom in this...

You have just very gently exhaled a helium atom in this room. Calculate how long ( $t$ in seconds) it will take to diffuse with a reasonable probability to some point on a spherical surface of radius $R=1$ meter surrounding your head.

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Key Concepts

Order-of-Magnitude Estimation

Order-of-magnitude estimation is a calculation approach that provides approximate values using simplified formulas and approximate constants. For diffusion problems, it involves using scaling relationships such as t ? R²/D to estimate the time required for particles to spread over a characteristic distance.

Mean Square Displacement

Mean square displacement is a statistical measure representing the average squared distance travelled by particles undergoing diffusion. In many cases, it is related to time by an expression such as ?r²? ? Dt (or with dimensionality-dependent factors), linking the spatial spread to the diffusion coefficient and elapsed time.

Diffusion Coefficient

The diffusion coefficient is a parameter that quantifies the rate at which a substance diffuses through a medium. It depends on factors such as the temperature, the viscosity of the medium, and the size of the diffusing particles, and appears in equations predicting the spread of particles over time.

Diffusion

Diffusion is the process by which particles spread from regions of high concentration to low concentration due to random thermal (Brownian) motion. It underlies many transport phenomena in physics, biology, and chemistry, and is characterized by the random movement of individual particles.

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