The uncertainties in the velocities of partic | vedclass

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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

$2$

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(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:

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