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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
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The wavelength of a probe is roughly a measure of the size of a structure that it can probe in some detail. The quark structure of protons and neutrons appears at the minute length-scale of 10–15 m or less. This structure was first probed in early 1970’s using high energy electron beams produced by a linear accelerator at Stanford, USA. Guess what might have been the order of energy of these electron beams. (Rest mass energy of electron = 0.511
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Find the typical de Broglie wavelength associated with a He atom in helium gas at room temperature (27 °C) and 1 atm pressure; and compare it with the mean separation between two atoms under these
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Compute the typical de Broglie wavelength of an electron in a metal at 27 °C and compare it with the mean separation between two electrons in a metal which is given to be about 2 × 10–10 m. [Note: Exercises 35 and 36 reveal that while the wave-packets associated with gaseous molecules under ordinary conditions are non-overlapping, the electron wave-packets in a metal strongly overlap with one another. This suggests that whereas molecules in an ordinary gas can be distinguished apart, electrons in a metal cannot be distintguished apart from one another. This indistinguishibility has many fundamental implications which you
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Answer the following questions: Quarks inside protons and neutrons are thought to carry fractional charges [(+2/3)e ; (–1/3)e]. Why do they not show up in Millikan’s oil-drop
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Answer the following questions: What is so special about the combination e/m? Why do we not simply talk of e and m
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Answer the following questions: Why should gases be insulators at ordinary pressures and start conducting at very low
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Answer the following questions: Every metal has a definite work function. Why do all photoelectrons not come out with the same energy if incident radiation is monochromatic? Why is there an energy distribution of
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Answer the following questions: The energy and momentum of an electron are related to the frequency and wavelength of the associated matter wave by the relations: E = h ν, p = λ h But while the value of λ is physically significant, the value of ν (and therefore,
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A particle is dropped from a height H. The de Broglie wavelength of the particle as a function of height is proportional
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The wavelength of a photon needed to remove a proton from a nucleus which is bound to the nucleus with 1 MeV energy is
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Consider a beam of electrons (each electron with energy E0) incident on a metal surface kept in an evacuated chamber.
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Consider Fig. Suppose the voltage applied to A is increased. The diffracted beam will have the maximum at a value of θ that
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A proton, a neutron, an electron and an α-particle have same energy. Then their de Broglie wavelengths compare
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An electron is moving with an initial velocity ` v = v_0hat i` and is in a magnetic field 0 `B=B_ 0hatj`. Then it’s de Broglie
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An electron (mass m) with an initial velocity `V=v_0hati(v_0 > 0)` is in an electric field 0 0 ˆ `E = –E_0hati ( E_0constant > 0)` . It’s de Broglie wavelength at time t is given
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An electron (mass m) with an initial velocity ` v = v_0hat i` is in an electric field `E=E_0hatj`. If `λ_0 = h/(mv_0)`, it’s de Breoglie wavelength at time t is given
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Relativistic corrections become neccssary when the expression for the kinetic energy `1/2mv^2` , becomes comparable with mc2, where m is the mass of the particle. At what de Broglie wavelength will relativistic corrections become important for an
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Two particles A1 sand A2 of masses m1, m2 (m1 > m2) have the same de Broglie wavelength.
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The de Broglie wavelength of a photon is twice the de Broglie wavelength of an electron. The speed of the electron is `V_e=c/100`.
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