UPSC Civil Services (Mains), Chemistry optional · 2026 · Paper I

Q5(a). de Broglie wavelength of a baseball

Question

What is the de Broglie wavelength for a baseball (140 g) moving at 40 m s⁻¹? Comment on your finding.

λ=h/mv=1.18×10⁻³⁴ m, far too small to detect, so a baseball shows no wave behaviour.

Momentum: p=mv=0.140×40=5.60 kg m s⁻¹
λ=h/mv=6.626×10⁻³⁴ J s5.60 kg m s⁻¹=1.18×10⁻³⁴ m
this is about 10¹⁹ times smaller than a nucleus ( 10⁻¹⁵ m). No slit or crystal is fine enough to diffract such a wave, so a baseball moves exactly as classical mechanics predicts.
The wave nature shows only for small masses: an electron accelerated through 100 V has λ=0.12 nm, close to atom spacings, and is diffracted by crystals.

The full model answer

Written out in full, as it should go in the answer booklet. The solution page with its diagrams follows it.

Given: m=140 g =0.140 kg; v=40 m s⁻¹; h=6.626×10⁻³⁴ J s.

Momentum: p=mv=0.140×40=5.60 kg m s⁻¹
λ=h/mv=6.626×10⁻³⁴ J s5.60 kg m s⁻¹=1.18×10⁻³⁴ m
Comment: this is about 10¹⁹ times smaller than a nucleus ( 10⁻¹⁵ m). No slit or crystal is fine enough to diffract such a wave, so a baseball moves exactly as classical mechanics predicts.
The wave nature shows only for small masses: an electron accelerated through 100 V has λ=0.12 nm, close to atom spacings, and is diffracted by crystals.

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