A $1 g$ baseball moves with a speed of $30 m s^{- 1}$ . Estimate its de Broglie wavelength and comment on the observability of wave effects for such a macroscopic object.

medium 3 marks Class 12 · Physics · Dual Nature of Radiation and Matter

Answer

The wavelength is

\approx 2 \times 1 0^{- 32} m

, far too small to observe any wave behaviour.

The correct answer is The wavelength is $\approx 2 \times 1 0^{- 32} m$ , far too small to observe any wave behaviour. — Because the wavelength is many orders of magnitude below any measurable length scale, diffraction or interference effects are essentially impossible to detect for the baseball.

Step-by-step solution

Convert the mass to kilograms: $m = 1 g = 1 \times 1 0^{- 3} kg$ .
Momentum $p = m v = (1 \times 1 0^{- 3}) (30) = 3.0 \times 1 0^{- 2} kg m s^{- 1}$ .
de Broglie wavelength $λ = \frac{h}{p} = \frac{6.626 \times 1 0 ^{- 34}}{3.0 \times 1 0 ^{- 2}} = 2.21 \times 1 0^{- 32} m$ .
Atomic dimensions are of order $1 0^{- 10} m$ ; the baseball wavelength is $\sim 1 0^{22}$ times smaller.
Because the wavelength is many orders of magnitude below any measurable length scale, diffraction or interference effects are essentially impossible to detect for the baseball.

Common mistake: Using the speed of sound or forgetting to convert grams to kilograms before computing momentum.

Concept tested: Matter wave wavelength for macroscopic objects

Published 11 September 2026 · How this solution was prepared and checked

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A 1 g baseball moves with a speed of 30 ms−1. Estimate its de Broglie wavelength and comment on the observability of wave effects for such a macroscopic object.

Step-by-step solution

A $1 g$ baseball moves with a speed of $30 m s^{- 1}$ . Estimate its de Broglie wavelength and comment on the observability of wave effects for such a macroscopic object.