The uncertainties in the velocities of partic | vedclass

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

Question

(A) According to Heisenberg's uncertainty principle,$\Delta x 	imes m \Delta v = \frac{h}{4\pi}$.For particle $A$: $\Delta x_A 	imes m_A 	imes \Del

Vedclass · Accepted Answer

$2$

Vedclass · Answer

(A) According to Heisenberg's uncertainty principle,$\Delta x 	imes m \Delta v = \frac{h}{4\pi}$.For particle $A$: $\Delta x_A 	imes m_A 	imes \Delta v_A = \frac{h}{4\pi}$.Given $\Delta v_A = 0.05 \, m/s$ and $m_A = m$,so $\Delta x_A 	imes m 	imes 0.05 = \frac{h}{4\pi} \dots (1)$.For particle $B$: $\Delta x_B 	imes m_B 	imes \Delta v_B = \frac{h}{4\pi}$.Given $\Delta v_B = 0.02 \, m/s$ and $m_B = 5m$,so $\Delta x_B 	imes 5m 	imes 0.02 = \frac{h}{4\pi} \dots (2)$.Dividing equation $(1)$ by equation $(2)$:$\frac{\Delta x_A 	imes m 	imes 0.05}{\Delta x_B 	imes 5m 	imes 0.02} = \frac{h/4\pi}{h/4\pi} = 1$.$\frac{\Delta x_A}{\Delta x_B} 	imes \frac{0.05}{0.1} = 1$.$\frac{\Delta x_A}{\Delta x_B} 	imes 0.5 = 1$.$\frac{\Delta x_A}{\Delta x_B} = \frac{1}{0.5} = 2$.

The uncertainties in the velocities of particles $A$ and $B$ are $0.05 \, m/s$ and $0.02 \, m/s$,respectively. If the mass of particle $B$ is five times that of particle $A$,then the ratio of the uncertainties in their positions $\left( \frac{\Delta x_A}{\Delta x_B} \right)$ is equal to:

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 .......

Quantum numbers of an atom can be defined on the basis of

The effect of the uncertainty principle is significant only for the motion of microscopic particles and is negligible for macroscopic particles. Justify the statement with the help of a suitable example.

The uncertainty in the position of an electron is $10 \ \mathring{A}$. Find the uncertainty in its velocity.

The uncertainty of velocity of an electron is $5.7 \times 10^5 \ m \ s^{-1}$. Find its uncertainty in position.

Vedclass Test Series

Exam Paper Generator

Online Exam Module