Final answer:
An intensity data/correlation function graph for small particles shows a rapid decay because they diffuse faster, resulting in a steep slope, whereas for big particles the decay is slower and the graph slope is more gradual due to their slower diffusion.
Step-by-step explanation:
When discussing an intensity data/correlation function graph concerning the behavior of particles, we are often talking about data from experiments like dynamic light scattering (DLS) or similar techniques in physics. These techniques are applied to determine the size of particles in a sample by measuring the fluctuations in light scattering due to Brownian motion of the particles.
In general, for small particles, the intensity autocorrelation function will decay more rapidly because small particles diffuse faster than big particles. Therefore, their motion leads to faster changes in the scattered light intensity, resulting in a steeper slope on the intensity autocorrelation graph as a function of time. This is due to the fact that the diffusion coefficient is inversely related to the particle size based on the Stokes-Einstein equation.
For larger particles, the decay in the autocorrelation function of the scattered light intensity occurs more slowly. This reflects the slower diffusion of larger particles, and consequently, the graph will show a more gradual slope. The intensity of scattered light will change less rapidly over time, resulting in a more extended correlation time.
These differences in the intensity correlation function are attributed to the different rates at which particles diffuse through the medium, which is a key characteristic used in particle sizing technologies. The graphs you might examine for such observations can be complex, but they will clearly present these differences in decay time as a vision of how size impacts particle dynamics.