Indicate whether each statement is true or false: (a) The band gap of a semiconductor decreases as the particle size decreases in the \(1-10-\mathrm{nm}\) range. (b) The light that is emitted from a semiconductor, upon external stimulation, becomes longer in wavelength as the particle size of the semiconductor decreases.

In nano-sized semiconductors, as the particle size decreases, the confinement of the electrons and holes within the material increases. This phenomenon is called quantum confinement. When quantum confinement comes into the picture, the bandgap between the valence and conduction bands become wider than that of bulk semiconductors. As a result, the band gap of a semiconductor increases as the particle size decreases in the \(1-10-\mathrm{nm}\) range. Therefore, the statement is False.

When external stimulation, such as electric energy or light, is applied to a semiconductor, it can emit light. The emitted light wavelength is influenced by the energy gap between the conduction and valence bands. From statement (a), we know that the band gap increases with a decrease in particle size, meaning that the energy difference between the valence and conduction bands becomes bigger. The relationship between energy and wavelength is given by \(E=\dfrac{hc}{\lambda}\), where \(E\) is the energy, \(h\) is the Planck's constant, \(c\) is the speed of light, and \(\lambda\) is the wavelength. As energy increases, the wavelength decreases. Therefore, as the particle size of the semiconductor decreases, the energy gap becomes larger and the emitted light wavelength becomes shorter, not longer. Thus, the statement is False.