The de Broglie wavelength of a non-relativistic particle is reduced by 20% by increasing its kinetic energy. The particle itself is unchanged. By what percentage has its kinetic energy increased?
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Question

The de Broglie wavelength of a non-relativistic particle is reduced by 20% by increasing its kinetic energy. The particle itself is unchanged. By what percentage has its kinetic energy increased?

G1 Physics · Accepted Answer

The new wavelength is λ₂ = 0.80λ₁. For fixed mass, K is inversely proportional to λ². Therefore, K₂ ÷ K₁ = (λ₁ ÷ λ₂)² = (1 ÷ 0.80)² = 1.5625. Thus the fractional increase in kinetic energy is 1.5625−1 = 0.5625. Percentage increase: 0.5625×100 = 56.25%. Correct option: C.