Video Lecture
Theory For Notes Making
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Objective Assignment
1.
A photon of frequency v has a momentum associated with it. If c is the velocity of light, this momentum is
(a) \frac{{hv}}{{{{c}^{\mathbf{2}}}}}
(b) \frac{{hv}}{c}
(c) \frac{v}{c}
(d) hvc
Ans (b)
2.
The de Broglie wavelength of thermal neutrons at ordinary temperature T K is
(a) \frac{{30.8}}{{\sqrt{T}}}\text{{ }\!\!\mathrm{\AA}\!\!\text{ }}
(b) \frac{{28.7}}{{\sqrt{T}}}\text{{ }\!\!\mathrm{\AA}\!\!\text{ }}
(c) \frac{{10.1}}{{\sqrt{T}}}\text{{ }\!\!\mathrm{\AA}\!\!\text{ }}
(d) \frac{{20.2}}{{\sqrt{T}}}\text{{ }\!\!\mathrm{\AA}\!\!\text{ }}\text{.}
Ans (a)
3.
The momentum of an X-ray photon of wavelength 0.10 nm will be
(a) 6.62 x 10-34 kg-m/s
(b) 3.31 x 10-24 kg-m/s
(c) 3.31 x 10-34 kg-m/s
(d) 6.62 x 10-24 kg-m/s
Ans (d)
4.
If E1, E2 and E3 are there respective kinetic energies of an electron, an alpha particle and a proton each having the same de Broglie wavelength, then
(a) {{E}_{1}}>{{E}_{3}}>{{E}_{2}}
(b) {{E}_{2}}>{{E}_{3}}>{{E}_{1}}
(c) {{E}_{1}}>{{E}_{2}}>{{E}_{3}}
(d) {{E}_{1}}={{E}_{2}}={{E}_{3}}.
Ans (a)
5.
The de Broglie wavelength of an atom of mass m at absolute temperature T is
(a) \frac{h}{{mkT}}
(b) \frac{h}{{\sqrt{{2mkT}}}}
(c) \frac{h}{{\sqrt{{3mkT}}}}
(d) \frac{h}{{3mkT}}.
Ans (c)
Subjective Assignment
Q.1
Write the following radiations in ascending order in respect of their frequencies :
Q.2
What is the frequency of electromagnetic waves produced by oscillating charge of frequency v ?
Q.3
How are infra-red waves produced ? What is the range of their wavelength ?
Q.4
Name the physical quantity which remains same for microwaves of wavelength 1 mm and UV radiations of 1600 Å in vacuum.
Q.5
Calculate the ratio of the accelerating potential required to accelerate
(a) a deuteron and
(b) an -particle to have the same de-Broglie wavelength associated with them. (Given : mass of deuteron = \displaystyle 3.2\,\,\,\times \,{{10}^{{-27}}} kg; mass of -particle = \displaystyle 6.4\,\times \,{{10}^{{-27}}} kg)
Q.6
Crystal diffraction experiments can be performed either by using electrons accelerated through appropriate voltage, or by using X-rays. If the wavelength of these probes (electrons or X-rays) is 1 Å, estimate which of the two has greater energy.
Q.7
An electron is accelerated through a potential difference of 100 volts. What is the de-Broglie wavelength associated with it ? To which part of the electromagnetic spectrum does this value of wavelength correspond ?
Q.8
Find the ratio of the de Broglie wavelengths, associated with
(a) Protons, accelerated through a potential of 128 V, and
(b) -particles, accelerated through a potential of 64V.
Q.9
An electron and a photon each have a wavelength of 2nm. Find (i) their moments (ii) the energy of the photon. (iii) the kinetic energy of the electron.
Q.10
What is the de Broglie wavelength of
(a) a bullet of mass 0.040 kg travelling at the speed of 1.0 km/s,
(b) a ball of mass 0.060 kg moving at a speed of 1.0 m/s, and
(c) a dust particle of mass 1.0 × 10–9 kg drifting with a speed of 2.2 m/s?
Q.11
An electron and a photon each have a wavelength of 1.00 nm. Find
(a) their momenta,
(b) the energy of the photon, and
(c) the kinetic energy of electron.
Q.12
(a) For what kinetic energy of a neutron will the associated de Broglie wavelength be 1.40 × 10–10m?
(b) Also find the de Broglie wavelength of a neutron, in thermal equilibrium with matter, having an average kinetic energy of (3/2) k T at 300 K.
Q.13
Obtain the de Broglie wavelength associated with thermal neutrons at room temperature (27 ºC). Hence explain why a fast neutron beam needs to be thermalised with the environment before it can be used for neutron diffraction experiments.
Q.14
Explain de Broglie dualistic nature of matter and derive de-Broglie relationship for wavelength of matter waves.
Q.15
What are matter waves ? Show that de-Broglie wavelength associated with an electron of energy, V-electron volt is approximately \displaystyle \frac{{12.27}}{{\sqrt{V}}}{\AA}.
Q.16
How can de-Broglie wave hypothesis be verified experimentally ? or Describe Davission and Germer experiment to establish the wave nature of electrons.
Q.17
An electron microscope uses electrons accelerated by a voltage of 50 kV. Determine the de Broglie wavelength associated with the electrons. If other factors (such as numerical aperture, etc.) are taken to be roughly the same, how does the resolving power of an electron microscope compare with that of an optical microscope which uses yellow light?
Q.18
X-rays, microwaves, UV rays and radio waves.