The relationship between the frequency of infrared IR radiation and the type of molecular vibrations observed in a sample of organic compound can be explained through the concept of vibrational spectroscopy. Infrared spectroscopy is a technique used to study the vibrational motions of molecules in organic compounds. When a molecule absorbs IR radiation, it undergoes a change in its vibrational energy levels, leading to different types of molecular vibrations.There are two main types of molecular vibrations: stretching and bending. Stretching vibrations involve a change in the bond length between two atoms, while bending vibrations involve a change in the bond angle between three atoms. These vibrations can be further classified as symmetric or asymmetric, depending on the displacement of the atoms involved.The frequency of the IR radiation absorbed by a molecule is directly related to the type of molecular vibration it undergoes. Each type of vibration has a characteristic frequency range, which depends on the strength of the chemical bond and the masses of the atoms involved. For example, stronger bonds and lighter atoms generally result in higher vibrational frequencies.In summary, the relationship between the frequency of infrared radiation and the type of molecular vibrations observed in a sample of organic compound is that the frequency of the absorbed IR radiation corresponds to the energy required for a specific type of molecular vibration stretching or bending to occur. By analyzing the IR spectrum of an organic compound, chemists can identify the functional groups present in the molecule and gain insights into its structure and properties.