Question

The uncertainty in the positions of an electron and proton is equal, the ratio of the uncertainties in the velocity of an electron and proton is:

• A. ${10}^3:1$
• B. $1:1836$
• C. $3672:1$
• D. $1836:1$

Answer 1

Answer: (D)

$1836:1$

Use , $\Delta v=\frac{h}{4\pi m}\Delta x$.

For electron, $\Delta v_{e^{-}}=\frac{h}{4\pi m_{e^{-}}}\Delta x$.

For proton, $\Delta v_{p^{+}}=\frac{h}{4\pi m_{p^{+}}}\Delta x$.

$\therefore$ $\frac{\Delta v_{e^{-}}}{\Delta v_{p^{+}}}=\frac{m_{p^{+}}}{m_{e^{-}}}=\frac{1.67\times {10}^{-27}}{9.1\times {10}^{-31}}=1836:1$