Question

Why Heisenberg uncertainty principle is not applicable for a bigger molecule?

Answer 1

Heisenberg's Uncertainty Principle:

1. By Heisenberg's principle, we know $\Delta x.\Delta p>=\frac{h}{4\pi }$where $∆p=m∆v$ (for slow-moving particles with respect to the speed of light). $\Delta x$ is the position, $\Delta p$is the momentum, and $h$ is Planck's constant.
2. $\Delta v$ is the uncertainty in the measurement of the velocity and mass($m$) is assumed to be constant, so the equation is $\Delta x\Delta v\ge \frac{h}{4\pi m}$
3. If $\Delta x$ is the error in position measurement and $\Delta p$ is the error in the measurement of momentum, then$\begin{array}{l}\mathrm{\Delta }X\times \mathrm{\Delta }p\ge \frac{h}{4\pi }\end{array}$
4. Since momentum, $∆p=m∆v$, Heisenberg’s uncertainty principle formula can be alternatively written as-$\begin{array}{l}\mathrm{\Delta }X\times \mathrm{\Delta }mv\ge \frac{h}{4\pi }\end{array}$
5. $\begin{array}{l}\mathrm{\Delta }X\times \mathrm{\Delta }m\times \mathrm{\Delta }v\ge \frac{h}{4\pi }\end{array}$Where, $\Delta v$ is the error in the measurement of velocity and assuming mass remaining constant during the experiment,$\begin{array}{l}\mathrm{\Delta }X\times \mathrm{\Delta }V\ge \frac{h}{4\pi m}\end{array}$
6. Accurate measurement of position or momentum automatically indicates larger uncertainty (error) in the measurement of the other quantity.
7. According to his theory, we can't measure the position and the velocity of the object accurately at the same time
8. From the formula, as the momentum is not low, the uncertainty in the momentum is low.
9. As Planck's constant is very small, it is very difficult to determine experimentally the uncertainties in the position and momentum of large objects.
10. A phenomenon like the atomic process and displacement are critically applicable.
11. Therefore the Heisenberg uncertainty principle is significant only for the smaller particles.
12. By using the uncertainty principle both the position and momentum of the particle cannot be measured simultaneously.
13. So Heisenberg's uncertainty principle is not applicable for a bigger molecule.