Albert Einstein proposed and experiment and produced anequation that could be used to confirm the existence of atoms and to determine how big they are.explosion that confirmed the existence of atoms and its size.example of atoms' existence and a model that determined how big they are.

Answer 1

Albert Einstein's contributions to atomic theory largely stemmed from his work on Brownian motion, which provided empirical evidence for the existence of atoms. In 1905, he published a paper explaining the random movement of particles suspended in a fluid (such as pollen grains in water). This phenomenon, known as Brownian motion, was empirically observed by botanist Robert Brown in 1827 but had not been explained until Einstein's work.

Explanation of Brownian Motion

Einstein's equation related to Brownian motion demonstrated that the movement of these suspended particles was due to collisions with the much smaller, invisible molecules of the fluid. By analyzing the statistical properties of the motion of these particles, Einstein provided a way to calculate the size of the molecules in the fluid, thereby confirming the existence of atoms and molecules.

Key Equation

Einstein derived an equation that described the mean square displacement of a particle undergoing Brownian motion:

\[ \langle x^2 \rangle = \frac{k_B T}{\pi \eta} t \]

Where:

• \(\langle x^2 \rangle\) is the mean square displacement of the particle.
• \(k_B\) is Boltzmann's constant.
• \(T\) is the absolute temperature.
• \(\eta\) is the viscosity of the fluid.
• \(t\) is the time.

This relationship implied that the movement of the particles could be quantitatively studied, which allowed for the estimation of atomic and molecular sizes.

Model and Size Estimation

The observations of particles undergoing Brownian motion and Einstein's theoretical framework led to important measurements. By examining the motion of pollen grains under a microscope, scientists were able to estimate the size of the atoms in the liquid, further confirming atomic theory.

Example of Atomic Existence:

• Electrical conductance: The flow of electricity in a conductor can be explained using the concept of free electrons, which are quantized and can be understood as discrete particles (atoms).

Model Determining Atomic Size:

• Atomic Models: The Rutherford model (1911) and later the Bohr model (1913) of the atom further refined our understanding of atomic structure, leading to the realization that atoms have a nucleus and electrons that occupy quantized orbits, with atomic radii typically on the order of angstroms (10^-10 meters).

Together, these theoretical insights and experimental confirmations solidified the existence of atoms and made it possible to estimate their sizes with increasing accuracy.