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A mosquito of mass 0.15mgis found to be flying at a speed of 50cm/swithin an uncertainty of 0.5mm/s.(a) How precisely may its position be known? (b) Does this inherent uncertainty present any hindrance to the application of classical mechanics?

Short Answer

Expert verified

a) By using uncertainty principle, the mosquito鈥檚 position is found to be 螖虫7.02脳10-25m.

b) In this scenario, the uncertainty principle has no bearing on the classical treatment since the wavelength of the mosquito is so short that it is difficult to detect experimentally.

Step by step solution

01

Given Information.

A mosquito of mass 0.15mg

Speed of 0.15mg

Uncertainty of0.5mm/s

02

Calculation for the Position of mosquito.

Given the uncertainty in the velocity, we need to work out the limit on the position measurement (螖虫).

螖p螖虫2m螖v螖虫2

m螖v螖虫2

0.15脳10-6办驳脳0.50脳10-3m/s脳螖虫1.054脳10-34办驳脳尘2s2

.螖虫1.054脳10-34m2脳7.5脳10-11

03

Whether uncertainty has any hindrance to classical mechanics.

Mosquitoes have a very low positional uncertainty, which is a feature of particles in general. In other words, the mosquito's associated wave is so little that the classical treatment of its motion provides a very close approximation to its true motion. To begin addressing the mosquito's wave nature, its mass must be at least somewhat comparable to that of the electron. As a result, the conclusion is that the uncertainty principle does not obstruct the classical treatment in this circumstance.

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