The optical properties of nanoparticles, particularly metallic nanoparticles like silver, are strongly influenced by their size. This is mainly due to the phenomenon called localized surface plasmon resonance LSPR . LSPR occurs when the conduction electrons in the nanoparticle oscillate collectively in response to the incident light. The oscillation frequency depends on the size, shape, and surrounding environment of the nanoparticles.When the size of silver nanoparticles changes, it affects their absorption and scattering of light in the visible spectrum in the following ways:1. Absorption peak shift: As the size of the silver nanoparticles increases, the absorption peak in the UV-Visible spectrum shifts towards longer wavelengths redshift . This is because larger nanoparticles have a higher number of conduction electrons, which leads to a stronger interaction with the incident light and a redshift in the LSPR peak.2. Scattering efficiency: The scattering efficiency of silver nanoparticles is also size-dependent. Smaller nanoparticles primarily absorb light, while larger nanoparticles are more efficient at scattering light. As the size of the nanoparticles increases, the scattering efficiency increases, and the ratio of scattering to absorption becomes larger. This is due to the increased interaction between the incident light and the larger surface area of the nanoparticles.3. Color changes: The color of a colloidal solution containing silver nanoparticles is also affected by the size of the nanoparticles. Smaller nanoparticles appear yellow, while larger nanoparticles can appear green, blue, or even purple. This color change is a result of the shift in the LSPR peak and the increased scattering efficiency of larger nanoparticles.4. Broadening of the absorption peak: As the size distribution of silver nanoparticles becomes broader, the absorption peak in the UV-Visible spectrum also broadens. This is because nanoparticles of different sizes have different LSPR frequencies, leading to a wider range of wavelengths being absorbed and scattered.In summary, changing the size of silver nanoparticles affects their absorption and scattering of light in the visible spectrum by shifting the LSPR peak, altering the scattering efficiency, causing color changes, and broadening the absorption peak. These size-dependent optical properties have significant implications for various applications, such as sensing, imaging, and photothermal therapy.