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Question

(C) According to Heisenberg's uncertainty principle: $\Delta x \cdot \Delta p \ge \frac{h}{4\pi}$.Given that the uncertainty in position and momentum

Vedclass · Accepted Answer

$ \frac{1}{2m} \sqrt{\frac{h}{\pi}} $

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(C) According to Heisenberg's uncertainty principle: $\Delta x \cdot \Delta p \ge \frac{h}{4\pi}$.Given that the uncertainty in position and momentum are equal, i.e.,$\Delta x = \Delta p$.Substituting this into the equation: $(\Delta p)^2 = \frac{h}{4\pi}$.Taking the square root on both sides: $\Delta p = \sqrt{\frac{h}{4\pi}} = \frac{1}{2} \sqrt{\frac{h}{\pi}}$.Since $\Delta p = m \cdot \Delta v$, we have $m \cdot \Delta v = \frac{1}{2} \sqrt{\frac{h}{\pi}}$.Therefore, the uncertainty in velocity is $\Delta v = \frac{1}{2m} \sqrt{\frac{h}{\pi}}$.

When uncertainty in position and momentum are equal, then the uncertainty in velocity is

Similar Questions

Assertion : It is impossible to determine the exact position and exact momentum of an electron simultaneously.
Reason : The path of an electron in an atom is clearly defined.

The uncertainty in the determination of the position of a small ball of mass $10 \ g$ is $10^{-33} \ m$. With what percentage of accuracy can its speed be measured, if it has a speed of $52.5 \ m \ s^{-1}$? (Given: $h = 6.6 \times 10^{-34} \ J \ s$)

What does the uncertainty principle state regarding the existence of a definite path or trajectory of an electron?

Choose the correct statement.

Which of the following is the correct formula for the Heisenberg uncertainty principle?

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