An electron is trapped within a square well potential of width 10 nm. What would be the wavelength of the photon emitted when an electron moves from the first energy level to the ground level.

Use energy difference between ground and first level to find E1-E0. Energy of the electron a nth energy level is found using En = (n^2pi^2hbar^2)/2mL^2Where n is the energy level plus 1, pi and hbar are constants, L is the width of the well in metres and m is the mass of the electron in kgFor E0 n=1 and E1 n=2 therefore E1-E0 = (3pi^2*(1.0510^-34)^2))/2(9.1110^-31)(1010^-9) = 1.810^-19 JThe energy can then converted to a wavelength using E=hf and c=flambda where h is Planck's constant, f is frequency in Hz and lambda is wavelength in metres and c is the speed of light constant This gives : E= hc/lambdaRe arrange to get lambda = hc/E = 1.10610^-6 metres or approximately 1.11 microns.