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**Previous Years JEE Advanced Questions**

**Paragraph for Question Nos. 1 to 3**

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 \mathrm{E}=\frac{\mathrm{p}^{2}}{2 \mathrm{m}}. Thus, the energy of the particle can be denoted by a quantum number ‘n’ taking values 1,2,3, … (n = l, 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} \mathrm{Js} \text { and } \mathrm{e}=1.6 \times 10^{-19} \mathrm{C}.