When a particle is restricted to move along x axis between x

Last updated: 6/13/2023

When a particle is restricted to move along x axis between x 0 and x a 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 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 p 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 x 10 34 Js and e 1 6 10 1 C V The allowed energy for the particle for a particular value of n is proportional to A a 2 1 C a 3 2 B a 2 D a 2009 If the mass of the particle is m 1 0 x 10 30 kg and a 6 6 nm the energy of the particle in 200