The size and shape of a metallic nanoparticle have a significant impact on its electronic and optical properties. This is mainly due to the phenomenon known as surface plasmon resonance SPR , which is the collective oscillation of electrons at the surface of a metal nanoparticle when excited by an external electromagnetic field.1. Electronic properties: As the size of a metallic nanoparticle decreases, the quantum confinement effect becomes more pronounced. This leads to an increase in the energy bandgap, which in turn affects the electrical conductivity and other electronic properties of the nanoparticle. The shape of the nanoparticle also influences the distribution of electrons on its surface, which can further impact its electronic properties.2. Optical properties: The optical properties of metallic nanoparticles are strongly influenced by their size and shape due to the SPR effect. The SPR frequency depends on the size and shape of the nanoparticle, as well as the dielectric properties of the surrounding medium. As a result, the absorption and scattering of light by the nanoparticle can be tuned by controlling its size and shape. This leads to unique optical properties, such as localized surface plasmon resonance LSPR and enhanced Raman scattering, which have applications in sensing, imaging, and photothermal therapy.The relationship between the size of a nanoparticle and its surface plasmon resonance frequency can be described as follows:- As the size of the nanoparticle decreases, the SPR frequency generally blue-shifts i.e., it moves towards shorter wavelengths . This is because smaller nanoparticles have a higher surface-to-volume ratio, which results in a stronger confinement of the surface plasmons and a higher SPR frequency.- The shape of the nanoparticle also affects the SPR frequency. For example, elongated nanoparticles such as nanorods exhibit two distinct SPR frequencies corresponding to the longitudinal and transverse plasmon modes. The longitudinal mode is red-shifted i.e., it moves towards longer wavelengths compared to the transverse mode, and its frequency is more sensitive to changes in the aspect ratio of the nanoparticle.In summary, the size and shape of a metallic nanoparticle play a crucial role in determining its electronic and optical properties, primarily due to the surface plasmon resonance effect. By controlling the size and shape of nanoparticles, it is possible to tune their SPR frequency and exploit their unique properties for various applications.