$A$ proton,an electron,and an alpha particle have the same kinetic energies. Their de-Broglie wavelengths will be compared as:

  • A
    $\lambda_{e} > \lambda_{p} > \lambda_{\alpha}$
  • B
    $\lambda_{\alpha} < \lambda_{p} < \lambda_{e}$
  • C
    $\lambda_{p} < \lambda_{e} < \lambda_{\alpha}$
  • D
    $\lambda_{p} > \lambda_{e} > \lambda_{\alpha}$

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$A$ proton and an electron are associated with the same de-Broglie wavelength. The ratio of their kinetic energies is:
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An electron beam has a kinetic energy equal to $100\; eV$. Find its wavelength (in $\mathring{A}$) associated with the beam,given the mass of an electron $= 9.1 \times 10^{-31}\; kg$,$1\; eV = 1.6 \times 10^{-19}\; J$,and Planck's constant $= 6.6 \times 10^{-34}\; Js$.

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The additional energy that should be given to an electron to reduce its de-Broglie wavelength from $1 \ nm$ to $0.5 \ nm$ is

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