## Highest precision in velocity

$\Delta p \Delta x\geq \frac{h}{4\pi }$

Martha Xuncax 3G
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### Highest precision in velocity

I was recently doing a problem that gave us the radius of 2 atoms and asked which atom could give us the highest precision of the velocity of the electron. The answer was the atom that had the greater radius, but I didn't really understand why. Does anyone know how to solve this?

Chem_Mod
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### Re: Highest precision in velocity

The larger radius increases the potential error when calculating the position because the area where the electron can be found is now larger and therefore less precise. According to the Heisenberg Uncertainty Principle, an increase in the error of position allows for more precision of momentum measurements, and therefore velocity measurements as well

Diego Zavala 2I
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### Re: Highest precision in velocity

Because of the uncertainty principle equation, $\Delta x\Delta p\geq h/4\pi$, $\Delta p$ is proportional to $(1/\Delta x)$

Hence, if Delta X increases than Delta p decreases and p=mv so velocity will also decrease