A pesky 1.7 mg mosquito is annoying you as you attempt to study physics in your

Question

A pesky 1.7 mg mosquito is annoying you as you attempt to study physics in your room, which is 4.5m wide and 2.5 m high. You decide to swat the bothersome insect as it flies toward you. but you need to estimate its speed to make a successful hit. A. What is the maximum uncertainty in the horizontal position of the mosquito? B. What limit does the Heisenberg uncertainty principle place on your ability to know the horizontal velocity of this mosquito? C. Is this limitation a serious impediment to your attempt to swat it?

Explanation / Answer

A)

The maximum uncertainty in horizontal direction is the length of the room.

?x­max = 4.5 m

B)

?xmax ?pmin > h/4?

?xmaxm ?vmin > h/4?

?vmin > h/4? m?xmax

?vmin > 6.626 x 10-34/4 x 3.14 x 1.7 x 10-3 x 4.5

?vmin > 0.06896049290204404479413846217893 x 10-31

?vmin > 6.896 x 10-33 m/s

C)

Yes it is a serious impediment in our attempt to swat it. When the mosquito moves with a speed greater than or equal to 6.896 x 10-33 m/s , the uncertainty in position reaches its maximum.

In normal situation the usual velocity of mosquito could be a few billion times more than 6.896 x 10-33 m/s so we cannot find its location using this principle for larger objects.

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