Word Count : 517

---

To derive Einstein's formula for the mean square displacement of a Brownian particle, we first need to understand the underlying principles of Brownian motion and the statistical mechanics involved.

Brownian motion is the random motion of particles suspended in a fluid due to collisions with the fluid molecules. This phenomenon was first observed by the botanist Robert Brown in 1827. Einstein provided a theoretical explanation for Brownian motion in 1905, which played a crucial role in confirming the atomic theory of matter.

Let's consider a Brownian particle of mass \(m\) suspended in a fluid at temperature \(T\). According to statistical mechanics, the mean square displacement (\( \langle x^2 \rangle \)) of the particle can be related to its diffusion coefficient (\(D\)) and the time interval (\(t\)) through the equation:

____ _________ ______ _____ ______ _____ ______ _____.
_________ _______ _______ _____ ____ _______.
____ __________ __________ ________ _________ _____ ________ ____ ______ ____ ____ _______.
___ _________ ________ _________ _______ __________ _____ ___ _______ ___ _______ ________.
__________ _____ __________ ______ ____ ___ ____.
_____ ________ _________ ________ ___.
______ ___ _______ _______ ___ _________ ________ _________.
______ ________ ____ ____ _____ ___ ___ _________ ______ __________ ____.
________ ___ ____ ________ ______ _______ _________ _________ ___.
________ _______ _____ _______ __________ ____ _____ __________ _____.
_____ ____ __________ ___ ______ _________ _____ ____ _________ _________.
________ __________ ___ ___ _________ _______ ___ _______ ______ _______ ________.
______ _____ _________ ___ ___ ______ _____ ________ ___ ______ _____ ______.
______ ____ ___ ___ _____ ___ ___.
__________ ________ ___ __________ ____.
___ _______ ___ ____ _____ ____ _____ ________ ___ _____ _________.
_________ _________ _____ ______ _________ _____ ________ _______ _________.
_____ _______ _____ _____ _____ __________ __________ ____ ________ ____ ____ ______.
________ ____ _________ _______ ________ ______ _________ ______ ___ ____ _______ ________.
__________ ________ _________ __________ __________ _______ ___ ______ _______ ________.
____ ___ _______ __________ __________.
_________ _________ ________ _________ ________ ___ ______ ________ ___ ___.
_______ ______ _____ _______ _____ ___.
__________ _________ ___ ___ ______ _______ _________ __________ ____ ____ ________ ____.
_________ ______ _________ _____ ____ _______ ________ ________ ____ ______.
_____ ____ ______ ____ _______ _______ _____ ____ ____ _____ __________.
____ ___ ____ ______ _________.
_______ _____ ______ ______ _________ _____ _____ _______.
_______ _________ ____ __________ _________ ______ _________ ______ _____ _______.
___ ______ ________ ________ _____ _____ ________ __________ ___ ___ ___.
___ _______ _________ ___ ________ ______ ___ _____ _____ ____ _____.
________ _____ ____ ____ _____ __________ _______ ______ ____ ______ __________.
_________ ________ ___ ________ _____ __________ _______ ___ __________ ________.
______ _________ _______ __________ _______ ___.
_______ _____ ____ ______ ____ ______ ______ _____.
_________ __________ _______ _____ __________ ______ ____ ___ ______ ____ ______ _______.
________ ___ _________ _______ _____ ___ ___ _______ _______.
_________ ___ __________ _________ __________ _____ ________ _________ _______.
______ _______ _______ _____ _____ _____ ______ _________.
__________ _______ ________ ______ _________.
__________ ________ ___ ______ _________ _________.
__________ _________ ____ ____ __________ ____ ______ __________ ___ _______.
________ ___ ________ ______ ____ __________ ___ _________ _________.
Get Full Answer on WhatsApp