Structure of Atom

Structure of Atom

Question

A stream of electrons from a heated filament was passed between two charged plates kept at a potential difference V esu. If e and m are charge and mass of an electron, respectively, then the value of h/λ (where λ is wavelength associated with electron wave) is given by:

  • 2meV

  • square root of mev
  • square root of 2 meV end root
  • mev

Answer

C.

square root of 2 meV end root

The relation between h/λ and energy is given as:
Applying de-Broglie wavelength and kinetic energy term in eV.
de-Broglie wavelength for an electron (λ) = h/p
⇒ p  = h/ λ       (i)
Kinetic energy of an electron = eV
As we know that,
KE space equals space fraction numerator straight p squared over denominator 2 straight m end fraction
therefore space eV space equals space fraction numerator straight p squared over denominator 2 straight m end fraction
space or space straight p space equals square root of 2 meV end root
From equations (i) and (ii), we get
straight h over straight lambda space equals space square root of 2 meV end root

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