According to Heisenberg uncertainty principle, x*p = h/4 where, p - the uncertai

Question

According to Heisenberg uncertainty principle,

x*p = h/4

where, p - the uncertainty in momentum;

x - the uncertainty in position

and Planck's Constant, h=6.626 X 10-34 m2kgs-1

Now, The uncertainty in momentum can be written as

p=mv , where

v - the uncertainty in velocity;

=2.275% of 84.50 m/s i.e. 1.922 m/s
m - the mass of the particle.

In the given case, we are dealing with 0.2574 kg base ball having an uncertainty in velocity is 1.922 ms-1

so, the uncertainty in momentum will be

p=0.2574 kg X 1.922 ms-1

=0.4947 kgms-1

Now, From the given equation we can calculate the uncertainty in position as

x = h/4.(1/p)

=(6.626 X 10-34 m2kg s-1/4 x 3.14 ).(1/0.4947 kg-1m-1s1)

=(6.626 X 10-34 m2kg s-1/12.56). (2.02 kg-1m-1s1)

=(0.527 X 10-34m2kg s-1).(2.02 kg-1m-1s1)

=1.064.X 10-34 m

Explanation / Answer

Heisenberg's uncertainty principle can be expressed mathematically as x*p = h/4, where x and p denote the uncertainty in position and momentum respectively and h is Planck's constant. What would be the uncertaintry in the position of a pitched baseball (mass = 0.2574 kg) that was traveling at a velocity of 84.50 m/s if the velocity has an uncertainty of 2.275%?

please explain step by step

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