When a particle is restricted to move along the 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=p2/2m. 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.
Take h=6.6×10−34Jsande=1.6×10−19C.
If the mass of the particle is m=1.0×10−30kg and radius, a = 6.6 nm, the energy of the particle in its ground state is closest to
When a particle is restricted to move along the 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=p2/2m. 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.
Take h=6.6×10−34Jsande=1.6×10−19C.
If the mass of the particle is m=1.0×10−30kg and radius, a = 6.6 nm, the energy of the particle in its ground state is closest to
The correct option is B 8 meV
E=h28a2m=(6.6×10−34)28×(6.6×10−9)2×10−30×1.6×10−19 = 8 meV
E=h28a2m=(6.6×10−34)28×(6.6×10−9)2×10−30×1.6×10−19 = 8 meV
