Question

The velocity of a particle is `5.8*10^5 "m/s"` . Calculate the uncertainty in its position. (Mass of particle=`9.1x10^(-28)"g"` , `h=6.63*10^(-34)`)?

Answer 1

You can use Heisenberg's Uncertainty Principle:

Explanation:

Assuming the particle moving along the x-axis we can use Heisenberg's Uncertainty Principle:
`DeltaxDeltap_x>=h/(4pi)`
where:
`x` is position
`p_x` is momentum;
`h` is Planck's Constant;
and the `Delta`s represent uncertainties.
With your data you can consider:

1] a perfect knowledge of the velocity, implying an uncertainty of zero in the momentum (assuming a constant mass): `Deltap_x=0`
This gives you an enormous value (tending towards `oo`) of the uncertainty in the position (you do not know where the particle is!!!);

2] The uncertainty in velocity will be `+-5.8xx10^5m/s` meaning that the velocity you have is only one of the velocities you measured (the highest, probably, with other measurement representing possible velocities in a certain range from `0` to `5.8xx10^5m/s`).
So `Deltap_x=(9.1xx10^-28)/1000*5.8xx10^5=5.28xx10^-25kgm/s`
and:
`Deltax>=h/(Deltap_x4pi)=9.99xx10^-11m`
considering that the radius of an atom is `~~10^-10m`!!!

3] I thought of an intriguing situation!!! Observing your velocity, I noticed that is quite high!!!
So, I thought to introduce an uncertainty in the momentum given by the difference between:
Classical momentum : `p_x=mv=(9.1xx10^-28)/1000*5.8xx10^5=5.28xx10^-25kgm/s`
Relativistic momentum :
`p_(xr)=(mv)/sqrt(1-v^2/c^2)=5.31xx10^-25kgm/s`
(where: `c=3xx10^8m/s` is the speed of light)
So `Deltap_x=`3xx10^-27kgm/s#

`Deltax>=h/(Deltap_x*4*pi)=1.76xx10^-8m`