Usain Bolt can run the 100 meters in under 10 seconds. Let's say he weighs 200lb,...

Usain Bolt can run the 100 meters in under 10 seconds. Let's say he weighs 200lb, give or take. Estimate his wavelength during a 100 meter race. Given your answer, is the wave-like nature of Usain Bolt observable? Will it play an important role in a 100m race?

Solutions

Expert Solution

From De-broglie hypothesis,

Matter wave associated with moving particle is given by

λ=hmv

where, h = planck's constant = 6.626 x 10^-34J-s

Given, distance covered by Usain Bolt = 100m in 10 secs.

so velocity v = distance/time = 100/10 = 10m/s

Mass m = 200lb = 90.718 kg

since 1lb = 0.4535kg

Wavelength associated with Usain Bolt during 100 m race

λ = 6.626 x 10^-34/(90.718*10) = 0.007303 x 10^-34 m

or λ = 7.303 x 10^-37 m

COMPARISON

The diameter of atom is of the order of 10^-10m

The diameter of hydrogen nucleus = 10^-15m

Smallest atom, it self is hardly observable through modern techniques like XRD (X-Ray Diffractioin) and TEM (Transmission Electron Microscopy). The wave associated with running Usain Bolt is far beyond the observable region and is almost impossible to observe.

This wavelength is extremely small, therefore Its affect is negligible and un-observable

genius_generous answered 1 year ago

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