Question

If the uncertainty in velocities of two particles A and B with mass $1.0\times {10}^{-27}kg$ and $1.0\times {10}^{-31}kg$ respectively is same, the ratio of uncertainty in the positions of A and B is :

• A. 1000:1
• B. 10,000:1
• C. 1:1000
• D. 1:10,000

Answer 1

The correct option is D 1:10,000

$\Delta xm\Delta v=\frac{h}{4\pi }$

$\Delta x_A{m}_A\Delta v_A=\Delta x_B{m}_B\Delta v_B$

But,

$\Delta v_A=\Delta v_B$

Hence,

$\Delta x_A{m}_A=\Delta x_B{m}_B$

$\Delta x_A\times 1.0\times {10}^{-27}kg=\Delta x_B\times 1.0\times {10}^{-31}kg$

$\frac{\Delta x_A}{\Delta x_B}=\frac{1.0\times {10}^{-31}kg}{1.0\times {10}^{-27}kg}=\frac{1}{10000}$