We calculate the Mössbauer spectrum of nuclei embedded in spheres of radius on the order of 1 μm which are suspended in a liquid. We demonstrate that the Mössbauer effect is an ideal means for testing the deductions based upon a generalized Langevin equation which takes into account the effects of acceleration memory on the force and torque of the liquid on a sphere and for studying, generally, the detailed statistical dynamical behavior of Brownian particles. The spectrum is expressed in terms of an integral over an integrand consisting of standard functions. Experimental desiderata are discussed and a list of sample experimental parameters given.