Planck's Constant and the size of the atom

[kirsten_2009]

Homework Statement

[/B]
If Planck’s constant were smaller than it is, how would the uncertainty principle be affected and how would the size of atoms be affected?

Homework Equations

The Attempt at a Solution

I know this question has been kind of asked before in this forum but an answer was never really concluded. Could you guys be so kind and let me know if my reasoning and answer are "correct"?

A:// Conceptually speaking; the uncertainty principle would be affected in that it’s “uncertainness” would be decreased because if the quanta of energy was smaller (since it was multiplied by a smaller number); it means that the space occupied by the field would be smaller and thus the position and/or velocity of an entity would be more accurately predicted since there is less space the species could actually be in.

With regards to the size of the atom; a smaller value for Planck’s constant would allow atoms to be smaller than presumed because the uncertainty of the electrons position (and velocity) would decrease and so the electron “cloud” could be narrowed down with increased accuracy and decreased error.

 

[andrevdh]

What course are you doing and what handbook or notes is used?

 

[kirsten_2009]

It's an introductory physics course focusing mainly on concepts (with some calculations of course). We are using Physics: Concepts and Connections by Art Hobson.

 

[andrevdh]

The principle itself would not be affected I would think, but the product of the uncertainties in the values
- position, momentum, energy and time - would. Neither would the size of atoms, just the values would
be known with less uncertainty.