When a particle is restricted to move along x-axis between x = 0 and x = 4, where a is of nanometer dimension, its energy can take only certain specific values. The allowed energies of the particle moving in such a restricted region, correspond to the formation of standing waves with nodes at its ends r = 0 and x= a. The wavelength of this standing wave is related to the linear momentum p of the particle according to the de-Broglie relation. The energy of the particle of mass m is related to its linear momentum as E= p^2//2m. Thus, the energy of the particle can be denoted by a quantum number 'r' taking values 1, 2, 3, ... (n = 1, called the ground state) corresponding to the number of loops in the standing wave. Use the model described above to answer the following three questions for a particle moving in the line x=0 to x=a. Take h=6.6 xx 10^(-34) Js and e=1.6 xx 10^(-19)C. The allowed energy for the particle for a particular value of n is proportional to