Electron beam when accelerated by a voltage of 10 kV , has a de-Broglie wavelength ' '. If the voltage is increased to 20 kV then the de-Broglie wavelength associated with the electron beam would be

Step-by-step solution

The de-Broglie wavelength for a particle with momentum p is given by = h/p , where h is Planck's constant. For an electron accelerated through potential difference V , the kinetic energy eV equals p^2/(2m) , yielding p = 2meV . Substituting into the wavelength formula gives = h/ 2meV . The wavelength scales as 1/ V . For voltages V₁ = 10 kV and V₂ = 20 kV , the ratio is: ₂ ₁ = V₁ V₂ = 10 20 = 1 2 Thus ₂ = / 2 , confirming that option D is correct.