The de Broglie wavelength for an electron accelerated through the potential difference of V₁ volt is ₁ . When the potential difference is changed to V₂ volt, the associated de Broglie wavelength is increased by 50 % . If (V₁/V₂) = (9/ ) , then the value of is __________.

Step-by-step solution

The de Broglie wavelength of an electron accelerated through a potential difference V is given by = h 2meV . This implies 1 V . Given that the new wavelength ₂ is increased by 50 % , we have ₂ = ₁ + 0.5 ₁ = 3 2 ₁ . Taking the ratio of the wavelengths, we get ₁ ₂ = V₂ V₁ . Substituting ₂ = 3 2 ₁ , we get 2 3 = V₂ V₁ . Squaring both sides yields V₂ V₁ = 4 9 , which gives V₁ V₂ = 9 4 . Comparing this with the given relation V₁ V₂ = 9 , we find = 4 . Answer: 4