Uncertainty in position and momentum are equa | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

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

Vedclass · Accepted Answer

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

Vedclass · Answer

(C) According to Heisenberg's uncertainty principle: $\Delta x \cdot \Delta p \geq \frac{h}{4\pi}$.Given that the uncertainty in position and momentum are equal,$\Delta x = \Delta p$.Substituting this into the equation: $(\Delta p)^2 = \frac{h}{4\pi}$.Therefore,$\Delta p = \sqrt{\frac{h}{4\pi}} = \frac{1}{2}\sqrt{\frac{h}{\pi}}$.Since $\Delta p = m \cdot \Delta v$,the uncertainty in velocity is $\Delta v = \frac{\Delta p}{m}$.Substituting the value of $\Delta p$: $\Delta v = \frac{1}{m} \cdot \frac{1}{2} \sqrt{\frac{h}{\pi}} = \frac{1}{2m} \sqrt{\frac{h}{\pi}}$.

Uncertainty in position and momentum are equal. Uncertainty in velocity is :-

Similar Questions

For a particle of mass $0.02 \, kg$,the uncertainty in its velocity is $9.218 \times 10^{-6} \, m/s$. The uncertainty in its position is .......

The uncertainty in the position of an electron is $1 \, \mathring{A}$. Find the uncertainty in its velocity.

Choose the correct statement.

Calculate the uncertainty in the position of a particle when the uncertainty in momentum is $1 \times 10^{-3} \, g \, cm \, sec^{-1}$.

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.

Vedclass Test Series

Exam Paper Generator

Online Exam Module