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Atoms and Nuclei question

2009 · Shift 1 · Q55

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JEE Advanced
Physics
Atoms and Nuclei
2009 · Shift 1 · Q55

Atoms and Nuclei question

2009 · Shift 1 · Q55

JEE AdvancedPhysicsAtoms and NucleiMCQ+3 / −1

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^2}} \over {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}}

J-s and

e = 1.6 \times {10^{ - 19}}

C.The speed of the particle, that can take discrete values, is proportional to

A
${n^{ - 3/2}}$
B
${n^{ - 1}}$
C
${n^{1/2}}$
D
$n$

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