The band gap in silicon is 1.12 eV. Calculate the maximum wavelength of electromagnetic radiation that results in promotion of electrons from the valence to the conduction band.

Tungsten (W) crystallizes in cubic structure. The edge length of the unit cell of this crystal structure is a = 3.1648 Å. Calculate the structure factor Fhkl for this crystal structure for the (110) and (200) planes. Here the scattering factor is fW (110) = 58 and fW (200) = 51. In this crystal structure, two W atoms are in (0,0,0) and (0.5,0.5,0.5) positions, respectively.

A laser contains a Ti:sapphire rod of length 5mm and composed of a material with n=1.76 and n2=1x10-19m2 w-1 The FWHM (intensity) beam diameter is 100µm, the average intra-cavity laser power is 8W, the pulse duration is 53fs and the pulse repetition frequency is 64MHZ. By considering the optical Kerr effect, by what distance (in nm) does the center of the beam lag behind the FWHM points after propagating the length of the rod?

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