An electron initially at rest is accelerated through a potential difference of 400 V. It then enters a second electric-field region that retards it through 300 V, but does not stop it. Neglect relativistic effects. If its de Broglie wavelength after retardation is N times its wavelength immediately after the first acceleration, find N.
Physics · Photoelectric effect and dual nature of matter · debroglie duel nature of light
JEE Mains NEET JEE Advanced

Question

An electron initially at rest is accelerated through a potential difference of 400 V. It then enters a second electric-field region that retards it through 300 V, but does not stop it. Neglect relativistic effects. If its de Broglie wavelength after retardation is N times its wavelength immediately after the first acceleration, find N.

Physics · Photoelectric effect and dual nature of matter · debroglie duel nature of light

G1 Physics · Accepted Answer

After acceleration through 400 V, the electron kinetic energy is K₁ = 400 eV. The opposing potential removes 300 eV, so after retardation: K₂ = 400−300 = 100 eV. For fixed mass, λ is inversely proportional to √K. Therefore, λ₂ ÷ λ₁ = √(K₁ ÷ K₂) = √(400 ÷ 100) = √4 = 2. Hence N = 2.