The phenomenon of Brownian motion is the random motion of...

The phenomenon of Brownian motion is the random motion of microscopically small particles as they are buffeted by the still smaller molecules of a fluid in which they are suspended. For a particle of mass $1.0 \times 10^{-16} \mathrm{kg},$ the fluctuations in velocity are of the order of $0.010 \mathrm{m} / \mathrm{s} .$ For comparison, how large is the change in this particle's velocity when the particle absorbs a photon of light with a wavelength of $660 \mathrm{nm}$ such as might be used in observing its motion under a microscope?

Key Concepts

Brownian Motion

Brownian motion refers to the erratic, random movement of small particles suspended in a fluid, resulting from collisions with the much smaller molecules of the surrounding medium. This phenomenon illustrates how microscopic interactions can lead to observed macroscopic motion, and it is a fundamental concept in statistical mechanics and thermodynamics.

Photon Momentum

Photon momentum is the concept that light, despite being massless, carries momentum that is inversely proportional to its wavelength. This momentum is given by the relation p = h/?, where h is Planck’s constant and ? is the wavelength. This principle is crucial in understanding phenomena where light interacts with matter, such as the minute changes in motion observed when a particle absorbs a photon.

Momentum Transfer by Absorption

When a particle absorbs a photon, the momentum carried by the photon is transferred to the particle. This transfer of momentum, according to the conservation of momentum, results in a change in the particle's velocity. Even though the photon has a very small momentum compared to everyday scales, the impact can be significant when the particle involved has a very low mass.

Velocity Change Calculation

The change in velocity of a particle due to the absorption of a photon is determined by the relation ?v = p/m, where p is the momentum transferred by the photon and m is the mass of the particle. This calculation illustrates how even tiny amounts of momentum, when imparted to an object of extremely small mass, can result in measurable velocity changes, making it a relevant consideration in microscopic experiments and observations.

Please give Ace some feedback