A Si sample with 1016 cm-3 donors is optically excited such that 1019 cm-3 electron/hole pairs are generated per second uniformly in the sample. The light causes the sample temperature to rise to 450 K. Find the quasi-Fermi levels upon shining the light on the sample. Electron and hole lifetimes are both 10 μs. Dp = 12 cm2/s, Dn = 36 cm2/s, ni = 1014 cm-3 at 450 K.

Awall of 0.5m thickness is to be constructed from a material which has average thermal conductivity of 1.4 w/mk. the wall is to be insulated with a material having an average thermal conductivity of 0.35 w/mk so that heat loss per square meter shall not exceed 1450 w. assume inner wall surface temperature of 1200°c and outer surface temperature of the insulation to be 15°c. calculate the thickness of insulation required.