2. Atomic interactions can be modeled using a variety of potential energy approximations. In a one-dimensional monatomic chain consisting of N atoms, the interaction energy between neighboring atoms can be expressed as U(y) 12 4l()" - (P1 Where and are constants specific to a given material, is the interatomic spacing given in units of Angstroms, and U(r) has units of eV atom. [15 points] (a) Calculate the interatomic spacing and interaction energy when in equilibrium. (b) Find the elasticity modulus (stiffness) of the monoatomic chain, only considering the interaction energy between neighboring atoms.