Use Heisenberg's Uncertainty Principle to calculate the uncertainty in the position of a 546 mg ball moving at a speed of 5.3 m/s if the speed is known to be correct within ±0.05 m/s. My...

Use Heisenberg's Uncertainty Principle to calculate the uncertainty in the position of a 546 mg ball moving at a speed of 5.3 m/s if the speed is known to be correct within

±0.05

m/s.

My book defines the formula as:

Delta x  *  Delta (mv)  >/    h/4pi

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llltkl | College Teacher | (Level 3) Valedictorian

Posted on

According to Heisenberg's uncertainty principle:

`Deltax*Delta(mv)gt=h/(4pi)`

`Deltax*mDeltavgt=h/(4pi)`

Here m=`546*10^-6` kg

`Deltav=0.05`

Plugging in the values,

`Deltaxgt=(6.626*10^-34)/(4pi*546*10^-6*0.05)`

`gt=1.93*10^-30 m`

In other words, the uncertainty in the position is at least `1.93*10^-30` meters.

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