Question

Which of the following is the most correct expression for Heisenberg's uncertainty principle:

• A. $\Delta x.\Delta p=\frac{h}{4\pi }$
• B. $\Delta x.\Delta p\ge \frac{h}{4\pi }$
• C. $\Delta x.\Delta p\le \frac{h}{4\pi }$
• D. $\Delta x.\Delta v=\frac{h}{4\pi }$

Answer 1

The correct option is B $\Delta x.\Delta p\ge \frac{h}{4\pi }$

Here answer is option B

The reduced plancks constant, is not represented by h but instead by $\hslash$ . I t is equal to $\frac{h}{2\pi }$

$\Delta p$ is the same as $m\Delta v$ (for$v<<c$) because $p=mv$

$\Delta x\times m\Delta v\approx h$

$\Delta x\Delta p\approx h$

which is another way of writing the uncertainity princilpe

The normal way to write is

$\Delta x\Delta p\ge \frac{h}{2\pi }$

$\hslash$ is the same as $\frac{h}{2\pi }$ so that can be rewritten as

$\Delta x\Delta p\ge \frac{h}{2\pi }$