Question

The ratio of uncertainties in the velocities of electron and proton is 1 : 2. Then the uncertainties in their positions are in a ratio of _______.

• A. 1 : 1837
• B. 3674 : 1
• C. 2 : 1
• D. 1 : 3674

Answer 1

Answer: (B)

3674 : 1

According to Heisenberg uncertainty principle,

$\Delta p\Delta x=\frac{h}{4\pi }$

$\Delta v\Delta x=\frac{h}{4\pi m}$ because $\Delta p=m\Delta v$

We have, $m_e=\frac{1}{1837}{m}_p$

$\frac{\Delta v_e}{\Delta v_p}=\frac{1}{2}$

Therefore, $\frac{\Delta x_e}{\Delta x_p}=\frac{\Delta v_p{m}_p}{\Delta v_e{m}_e}$

$\frac{\Delta x_e}{\Delta x_p}=\frac{3674}{1}$