For the element barium, which wavelength of light is produced by the largest drop in energy for an electron? which represents the smallest drop? explain.

For such calculation, we apply Planck's equation:
E = nhc / λ; where n is the number of photons, h is the Planck's constant, c is the speed of light and λ is the wavelength of the light.
As is visible from the equation, energy and wavelength have an inverse relationship. Therefore, larger energy drops produce smaller wavelengths and smaller drops produce larger wavelengths.