When a particle is restricted to move along x-axis between x=0 and x=a , where a is of nanometer dimesion , 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 node at its end 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 $E = \frac{p ^{2}}{2 m}$ . 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 allowed energy for the particle for a particular value of n is proportional to

Question

When a particle is restricted to move along x-axis between x=0 and x=a , where a is of nanometer dimesion , 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 node at its end 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 = \frac{p ^{2}}{2 m}

. 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 allowed energy for the particle for a particular value of n is proportional to

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