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JEE Main202325 Jan 2023Morning ShiftPhysicsDual Nature of MatterActual

Electron beam used in an electron microscope, when accelerated by a voltage of 20 kV has a de-Broglie wavelength of λ 0 . If the voltage is increased to 40 kV then the de-Broglie wavelength associated with the electron beam would be:

Options

  1. A3 λ 0
  2. B9 λ 0
  3. Cλ 0 2
  4. Dλ 0 2

Correct answer

D. λ 0 2

Step-by-step solution

The de-Broglie wavelength of an electron accelerated through potential V is λ = h m v = h 2   m ( KE ) = h 2   meV where, h is Planck's constant, e is charge of electron and m is mass of electron. From above relation, λ ∝ 1 V ∴   λ λ 0 = 20 40 ⇒   λ = λ 0 2 .

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