In: Physics
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?
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