IIT JEE Advanced 2009 Paper 1

Paragraph Type
This section contains 2 paragraphs. Based on each paragraph, there are 3 questions. Each question has 4 choices (A), (B), (C) and (D) out of which ONLY ONE is correct.
Paragraph for Questions 13–15:
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 × 10−34J−s and e =1.6 × 10−19C.