A non-relativistic particle of fixed mass is initially moving with speed v, and its de Broglie wavelength is measured to be 0.80 nm. The particle is then accelerated so that its speed becomes 25% greater than its initial speed, without changing its identity or mass. If the new de Broglie wavelength is (N ÷ 100) nm, find N.
Physics · Photoelectric effect and dual nature of matter · debroglie duel nature of light
JEE Mains NEET JEE Advanced

Question

A non-relativistic particle of fixed mass is initially moving with speed v, and its de Broglie wavelength is measured to be 0.80 nm. The particle is then accelerated so that its speed becomes 25% greater than its initial speed, without changing its identity or mass. If the 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

For a non-relativistic particle, λ = h ÷ (mv). Since h and m remain constant, λ is inversely proportional to v. The new speed is v₂ = 1.25v₁. Therefore, λ₂ ÷ λ₁ = v₁ ÷ v₂ = 1 ÷ 1.25 = 0.80. Hence, λ₂ = 0.80×0.80 nm = 0.64 nm. Thus, λ₂ = 64 ÷ 100 nm. Therefore N = 64.