An electron accelerated through a potential difference V₁ has a de-Broglie wavelength λ. When the potential is changed to V₂, its de-Broglie wavelength increases by 50%. The value of V₁/V₂ is:
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Question

An electron accelerated through a potential difference V₁ has a de-Broglie wavelength λ. When the potential is changed to V₂, its de-Broglie wavelength increases by 50%. The value of V₁/V₂ is:

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G1 Physics · Accepted Answer

For an electron accelerated through potential V, λ ∝ 1/√V. Thus λ₂/λ₁ = 1.5 = √(V₁/V₂). Squaring gives V₁/V₂ = 2.25 = 9/4.