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An object is moving along a straight line, and the uncertainty in its position is 2.20...

An object is moving along a straight line, and the uncertainty in its position is 2.20 m. (a) Find the minimum uncertainty in the momentum of the object. Find the minimum uncertainty in the object's velocity, assuming that the object is (b) a golf ball (mass = 0.0450 kg) and (c) an electron.

Solutions

Expert Solution

Uncertainity in position    Δx = 2.2 m

(a) according to uncertainity principle

Uncertainity in momentum    ΔP    =   h / (4πΔx)

Here   h = 6.63*10-34 J.s

plug all values we get

           ΔP    =    2.39*10-34 Kg m/s

(b) mass of the ball   m = 0.045 kg

     Uncetainity in velocity    ΔV    =   ΔP   / m      

                    ΔV    = 5.32*10-32 Kg . m/s

(c)   m   = mass of the electron    =   9.1*10-31 kg

Uncetainity in velocity of the electron  

     

                              ΔV    =   ΔP   / m      = (  2.39*10-34 Kg m/s ) /(9.1*10-31 kg   )  

                                           Δv   = 2.6210-4 Kg . m/s

genius_generous answered 1 year ago
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