# 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)#)?

##### 1 Answer

You can use Heisenberg's Uncertainty Principle:

#### Explanation:

Assuming the particle moving along the x-axis we can use Heisenberg's Uncertainty Principle:

where:

and the

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):

This gives you an enormous value (tending towards

2] The uncertainty in velocity will be

So

and:

considering that the radius of an atom is

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** :

**Relativistic momentum** :

(where:

So