1.Use the Heisenberg uncertainty principle to calculate x for an electron with v

Question

1.Use the Heisenberg uncertainty principle to calculate x for an electron with v = 0.580 m/s.

2.By what factor is the uncertainty of the (above) electron's position larger than the diameter of the hydrogen atom?
(Assume the diameter of the hydrogen atom is 1.00×10-8 cm.)

3.Use the Heisenberg uncertainty principle to calculate x for a ball (mass = 174 g, diameter = 6.40 cm) with v = 0.580 m/s.

4.The uncertainty of the (above) ball's position is equal to what factor times the diameter of the ball?

Explanation / Answer

1. deltax deltap > = h / (4 pi )

deltax x ( 9.109 x 10^-31 x 0.580 ) = (6.626 x 10^-34 ) / (4 x pi )

deltax = 9.98 x 10^-5 m

2. deltax / d = (9.98 x 10^-5 ) / (1 x 10^-8 x 10^-2 m ) = 998028 times

3. deltax x ( 0.174 x 0.580 ) = (6.626 x 10^-34 ) / (4 x pi )

deltax = 5.225 x 10^-34 m

4. deltax / diameter = (5.335 x 10^-34) / (6.40 x 10^-2) = 8.16 x 10^-33 time

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