Question

Consider a deuterium atom (1 electron orbiting one proton and one proton). Calculate the energy required to excite an electron in the H atom from the first (n = 2) excited state to the third (n = 4) excited state Calculate the wavelength of the corresponding photon required to create this excitation. Is it in the visible, ultraviolet, or infrared portion of the electromagnetic spectrum? Imagine a large single-crystal wafer of silicon (Si), where a Si atom is replaced by phosphorus (P). Draw a simplified projection of the 2D lattice of silicon, with the P atom in the middle Find the net charge of the P atom, and its 4 nearest and 4 next-nearest neighbors. Assuming the P atom donated one electron, and that the corresponding electron is far from it in the lattice, find the net charge of the P donor atom for itself only, itself plus its 4 nearest neighbors, and finally itself plus 4 nearest and 4 next-nearest neighbors. Consider a wafer of pure, single-crystal gallium arsenide (GaAs) Using expressions for the 3D direct-bandgap density of states and Fermi-Dirac distribution at a temperature T, sketch the total carrier concentration as a function of energy. How far from the conduction band minimum is the peak located, in terms of kT? Determine the temperature at which the intrinsic carrier concentration of GaAs is equal to that of crystalline silicon at room temperature (T = 300 K).

Answer 1

a) Total energy of the n" orbit is 72 For Deuterium Z -2, n-2 -13.6(2) =-13.6 eV -13.6(2) 3.4 eV Energy is, -- 3.4 eV +13.6 eV -10.2 eV b) Energy is, hc (1240 eVnm121.6 nm 10.2 eV The wavelength comes under the ultraviolet regiorn