U(R)NNU(R)+k(RRe)2En=h=(n+2k)CH353En=hion+2hwHomeworkassignment3(dueTuesdayFeb28) 1. A quantum model of a diatomic molecule. The simplest model of a diatomic molecule such as CO consists of two masses (atoms) connected by a spring obeying Hook's law (this model is commonly referred to as the "harmonic oscillator"). As discussed in class, the potential energy of the molecule is then given by U(R)U(Re)+ kx2/2, where x=RRe is the deviation of the bond length from its equilibrium value Re and k is a spring constant. According to quantum mechanics, the vibrational energy of such a contraption can only take on discrete values, En=h(n+21), where n=0,1,2,3 is any non-negative winteger. Here h=1.01034Js is Planck's constant and is the oscillation frequency of the molecule. This is all you need to know about quantum mechanics for the purpose of solving this problem. A Assuming that the frequency is known and that the molecule's surroundings are at temperature T. derive a formula describing the vibrational partition function q(T)=n=0eEn/(kDT) as a function of temperature [Note: the following identity may be useful: 1+a+a2+=1a1 for 0a