Question

Given : The mass of electron is $9.11\times {10}^{–31}kg$, Planck constant is $6.626\times {10}^{–34}Js$, the uncertainty involved in the measurement of velocity within a distance of $0.1\AA$ is:

• A. $5.79\times {10}^{5}m{s}^{-1}$
• B. $5.79\times {10}^{6}m{s}^{-1}$
• C. $5.79\times {10}^{7}m{s}^{-1}$
• D. $5.79\times {10}^{8}m{s}^{-1}$

Answer 1

The correct option is B $5.79\times {10}^{6}m{s}^{-1}$

From the formula of Heisenberg uncertainty principle, i.e., $\Delta p.\Delta x\ge \frac{h}{4\pi }$
Where; $\Delta p$ = uncertainty in momentum
$\Delta x$ = uncertainty in position
$h$ = planck’s constant
According to the formula; $\Delta p.\Delta x=\frac{h}{4\pi }$ where $\Delta p=m\Delta v$
⇒ $m\Delta v.\Delta x=\frac{h}{4\pi }$
⇒ $\Delta v=\frac{h}{4\pi \times m\times \Delta x}$
$\Delta v=\frac{6.626\times {10}^{-34}}{0.1\times 10-10)\times (9.11\times {10}^{-31})\times (4)\times (3.143)}$
= $5.79\times {10}^{6}m{s}^{-1}$