Question

6. Consider an electron in an infinite potential well of size 1 nm (a) What is the ground state (lowest energy level) energy of the electron? (b) What is the energy required to move an electron from ground state to the third energy level (n-3)? (c) What wavelength of photon would be emitted if the electron move from n-3 to its ground level? (Electron mass - 9.11 x 103 kg, h-1.055 x 1034 J.s, h 6.626 x 1034 J.s)

Answer 1

(a) energy of electro in any state in potential well is given by E = n^2 phi^2 h^2/2 m L^2. Here L = 1 nm = 1 times 10^minus 9 m For ground state n = 1. E_Gs = phi^2 h^2/2 m L^2. = (3.14)^2 times (1.055 times 10^minus 34)^2/2 times 3.111 times 10^minus 31 times (1 times 10^minus 9)^2 E_gs = 6.023 times 10^minus 20 J \r\n (b) Energy required to move the electron from ground state to third excited state is simply the difference between energies of this states so delta E = E_g minus E_1 = g phi^2 k^2/2 m L^2 minus phi^2 k^2/2 m L^2 = 8 phi^2 h^2/2 m L^2 = 4 phi^2 h^2/m L^2 = 4 times (3.14)^2 times (1.055 times 10^minus 34)^2/9.11 times 10^minus 31 (1 times 10^minus 9)^2 delta E = 4.82 times 10^minus 19 J