When a particle is restricted to move along x-axis between x=0 and x=a , where a is of nanometer dimesion , 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 node at its end x=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 $E=\frac{p^2}{2m}$ . Thus, the energy of the particle can be denoted by a quantum number 'n' 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 $h=6.6\times {10}^{-34}Js$ and $e=1.6\times {10}^{-19}C$.
If the mass of the particle is $m=1.0\times {10}^{-30}$ kg and a=6.6 nm, the energy of the particle in its ground state is closets to

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