Avogadro's no.-6.022x10a mole", h (plank constant) is-бабао, sec (35 points) the wave function for a particle moving along x axis between the limits 0 and 1) l is: ψ, (x)-c sin (nx x/l) where n are 1, 2.3 a) determine the normalization constant c b) why can't n take the value of 0, briefly explair c) for n-3 determine the values of x (in terms of l) that correspond to a maximum or a minimum in the wave function d) for n-3 determine the values of x (in terms of l) that correspond to a node. d/dx (sin ax) - a cos ax sin(ax) -0, then ax-n't where n's 0, 1, 2, 3 cos(ax) so, then axa π/2 + n'n where n'" 0, 1, 2, d/dx (cos ax)- -a sin ax jsin2 (ax) dx-x/2-1/4a (sin 2ax) 2) (80 points) the energy of quantum states in the particle in a box of lingth lis: n h derive the equation for the energy difference between successive states (n) and (n+1) a) estimate the energy difference between the two energy states 2 and 3 for an electron confined in a box with the dimension l of 15 nm (nanometer 1x10*m); mass of the electrons 9.109 x 10": determine the wavelength of the light required to achieve the excitation of the electron from state 2 to 3. (recall e-h c/a) where c is speed of light (3x10 m. sec) b) c) (10 points) the operator p, that is used to determine the momentum of a particle in a box is h/i (d/dx). the wave function for a particle moving along x axis between the limits 0 and lis: 3) show whether wn (x) is an eigenfunction of p given: d/dx (sin ax) a cos ax (15 points) knowing that general the condition of orthogonality is written as: 4)