Question

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

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

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