Write the Hamiltonian for the As atom. Use summation notation and specify limits

Consider the follow image of two waves (i.e., orange and black oscillatory curves). Note that the horizontal and vertical axes labels are the numbers on the straight lines intersecting at 0,0. a) What is the amplitude and wavelength of the black and orange lines? (Note the wavelength may be a whole number or a multiple of pi.) b) Write out the form of these two waves in terms of a sine or a cosine function times a constant (i.e. in form Asin(cx) or Acos(cx) ). c) What is the momentum of a photon associated with each of the two waves? You may assume the x-axis measures distance in units of nanometers.

Why is emission wavelength longer than absorption wavelength?  Please answer at your own words. Answer should be to the point.

Please do it fast