Question

A microscope using suitable photons is employed to locate an electron in an atom within a distance of 0$.1 \, \mathring{A}$. What is the uncertainty involved in the measurement of its velocity?

• A. $5.79\times10^{6} cm s^{-1}$
• B. $5.79\times10^{6} m s^{-1}$
• C. $5.79\times10^{10} cm s^{-1}$
• D. $5.79\times10^{10} m s^{-1}$

Answer 1

Answer: (B)

$\Delta x \Delta p=\frac{h}{4 \pi} \, or \, \Delta x m \Delta \upsilon=\frac{h}{4 \pi} \Rightarrow \Delta\upsilon=\frac{h}{4\pi \Delta x m}$
$\Delta \upsilon=\frac{6.626\times10^{-34}J s}{4\times3.14\times0.1\times10^{-10} m\times9.11\times10^{-31} k g}$
$=0.579\times10^{7} m s^{-1}\left(1 J=m^{2}s^{-2}\right)=5.79\times10^{6} m s^{-1}.$