The band gap of bulk silicon is 1.14 ev. a quantum dot can be modeled as an infinite square well in 3 dimensions, and the band gap is different for a quantum dot. consider a silicon particle that is a cube of size 4 nm. calculate the band gap for this particle, which is the energy difference between the lowest energy level of the electron in the conduction band and the highest energy level of the hole in the valence band using ε = 12, effective masses of electron = 0.35 and hole = 0.80 (in units of electron mass).

Air enters a gas turbine with two stages of compression and two stages of expansion at 100 kpa and 17°c. this system uses a regenerator as well as reheating and intercooling – the intercooler returns the air to the inlet temperature. the pressure ratio across each compressor is 4 ; 300 kj/kg of heat are added to the air in each combustion chamber; and the regenerator operates perfectly while increasing the temperature of the cold air by 20°c. determine the system’s thermal efficiency. assume isentropic operations for all compressor and the turbine stages and use constant specific heats at room temperature. (0.378)