Question

Suppose that the uncertainty in determining the position of an electron in an orbit is 0.6 Å. What is the uncertainty in its momentum?

Answer 1

Heisenberg's Uncertainty Principle states that There is a fundamental and inherent limit of precision by which two quantites can be measured.


There is one equation, which states that The product of uncertainties in position and momentum cannot be less than a certain value.



This means that the more precisely we can measure one quantity, the less precisely we will know the values of other quantity.


The mathematical form is:

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

Here,


$\Delta x = \text{Uncertainty in Position} \\ \\ \Delta p = \text{Uncertainty in Momentum} \\ \\ h = \text{Planck's Constant}$


The Particle under consideration is an electron. Our data is:

$h = 6.626 \times 10^{-34} \, \, J \, s \\ \\ \Delta x = 0.6 \, \, \AA = 6 \times 10^{-11} \, \, m$

For calculation purposes, we usually consider the minimum product of uncertainties, and we replace the $\geq$ sign with an equality one.


Now, we can find uncertainty in momentum:



$\Delta x . \Delta p = \frac{h}{4\pi} \\ \\ \\ \implies \Delta p = \frac{h}{4 \pi \Delta x} \\ \\ \\ \implies \Delta p = \frac{6.626 \times 10^{-34}}{4 \times \pi \times 6 \times 10^{-11}}\\ \\ \\ \implies \boxed{\Delta p \approx 8.79 \times 10^{-25} \, \, kg \, m/s}$


Thus, uncertainty in momentum is $8.79 \times 10^{-25} \, \, kg \, m/s$

Hope it helps
Purva
Brainly Community

Answer 2

Answer:

Heisenberg's Uncertainty Principle states that There is a fundamental and inherent limit of precision by which two quantites can be measured.

There is one equation, which states that The product of uncertainties in position and momentum cannot be less than a certain value.

This means that the more precisely we can measure one quantity, the less precisely we will know the values of other quantity.

The mathematical form is:

Here,

The Particle under consideration is an electron. Our data is:

For calculation purposes, we usually consider the minimum product of uncertainties, and we replace the sign with an equality one.

Now, we can find uncertainty in momentum:

Thus, uncertainty in momentum is