Question

If a suitable photon is employed to locate an electron $($ mass $=9.11\times 10^{-31}kg)$ in an atom within a distance of $10.98nm$, the uncertainty involved in the measurement of its velocity in $m{s}^{-1}$ is

• A. $\frac{1.6565\times 10^6}{\pi }$
• B. $\frac{1.6565\times 10^4}{\pi }$
• C. $\frac{1.6565\times 10^{-8}}{\pi }$
• D. $\frac{1.6565\times 10^8}{\pi }$

Answer 1

Answer: (B)

Given,

Mass of electron $=9.11\times 10^{-31}kg$

Position of electron $=10.98nm$

$=10.98\times 10^{-9}m$

Here, Planck constant $=6.63\times 10^{-34}Js$

$\Delta v=?$

According to Heisenberg uncertainty

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

$\therefore \Delta v=\frac{6.63\times 10^{-34}Js}{4\times \pi \times 9.11\times 10^{-31}kg\times 10.98\times 10^{-9}m}$

$\Delta v=\frac{1.6565\times 10^4}{\pi }$

$\Delta v=$ uncertainty in velocity of electron