1
IIT-JEE 2009 Paper 1 Offline
+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 allowed energy for the particle for a particular value of $$n$$ is proportional to

A
$${a^{ - 2}}$$
B
$${a^{ - 3/2}}$$
C
$${a^{ - 1}}$$
D
$${a^2}$$
2
IIT-JEE 2009 Paper 1 Offline
+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.

If the mass of the particle is $$m=1.0\times10^{-30}$$ kg and $$a=6.6$$ nm, the energy of the particle in its ground state is closest to

A
0.8 meV
B
8 meV
C
80 meV
D
800 meV
3
IIT-JEE 2008 Paper 1 Offline
+3
-1

Which one of the following statements is WRONG in the context of X-rays generated from a X-ray tube?

A
Wavelength of characteristic X-rays decreases when the atomic number of the target increases.
B
Cut-off wavelength of the continuous X-rays depends on the atomic number of the target.
C
Intensity of the characteristic X-rays depends on the electrical power given to the X-ray tube.
D
Cut-off wavelength of the continuous X-rays depends on the energy of the electrons in the X-ray tube.
4
IIT-JEE 2007 Paper 2 Offline
+3
-1

Electrons with de-Broglie wavelength $$\lambda$$ fall on the target in an X-ray tube. The cut-off wavelength of the emitted X-rays is

A
$$\lambda_{0}=\frac{2 m c \lambda^{2}}{h}$$
B
$$\lambda_{0}=\frac{2 h}{m c}$$
C
$$\lambda_{0}=\frac{2 m^{2} c^{2} \lambda^{3}}{h^{2}}$$
D
$$\lambda_{0}=\lambda$$
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