The uncertainties in the velocities of two pa | vedclass

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(A) According to Heisenberg's uncertainty principle: $\Delta x \cdot m \cdot \Delta v = \frac{h}{4 \pi}$.Let the mass of particle $A$ be $m_A = m$ and

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$2$

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(A) According to Heisenberg's uncertainty principle: $\Delta x \cdot m \cdot \Delta v = \frac{h}{4 \pi}$.Let the mass of particle $A$ be $m_A = m$ and the mass of particle $B$ be $m_B = 5m$.The uncertainties in velocities are $\Delta v_A = 0.05 \ m \ s^{-1}$ and $\Delta v_B = 0.02 \ m \ s^{-1}$.For particle $A$: $\Delta x_A \cdot m \cdot 0.05 = \frac{h}{4 \pi} \dots (i)$.For particle $B$: $\Delta x_B \cdot 5m \cdot 0.02 = \frac{h}{4 \pi} \dots (ii)$.Equating $(i)$ and $(ii)$ since both equal $\frac{h}{4 \pi}$:$\Delta x_A \cdot m \cdot 0.05 = \Delta x_B \cdot 5m \cdot 0.02$.$\Delta x_A \cdot 0.05 = \Delta x_B \cdot 0.10$.$\frac{\Delta x_A}{\Delta x_B} = \frac{0.10}{0.05} = 2$.

The uncertainties in the velocities of two particles $A$ and $B$ are $0.05 \ m \ s^{-1}$ and $0.02 \ m \ s^{-1}$ respectively. The mass of $B$ is five times that of mass $A$. What is the ratio of uncertainties $\left(\frac{\Delta x_A}{\Delta x_B}\right)$ in their positions?

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