A non-relativistic particle has a de Broglie wavelength of 0.40 nm. It undergoes an inelastic collision in which it loses 36% of its kinetic energy, but the particle itself is not transformed. If its new de Broglie wavelength is (N ÷ 100) nm, find N.
Physics · Photoelectric effect and dual nature of matter · debroglie duel nature of light
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Question

A non-relativistic particle has a de Broglie wavelength of 0.40 nm. It undergoes an inelastic collision in which it loses 36% of its kinetic energy, but the particle itself is not transformed. If its new de Broglie wavelength is (N ÷ 100) nm, find N.

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

G1 Physics · Accepted Answer

After losing 36% of its kinetic energy, the particle retains K₂ = 0.64K₁. For a non-relativistic particle, λ is inversely proportional to √K. Hence, λ₂ ÷ λ₁ = √(K₁ ÷ K₂) = 1 ÷ √0.64 = 1 ÷ 0.80 = 1.25. Therefore, λ₂ = 1.25×0.40 nm = 0.50 nm. Thus, λ₂ = 50 ÷ 100 nm. Hence N = 50.