Question

Assuming an electron is confined to a 1 nm wide region. Find the uncertainty in momentum using Heisenberg uncertainty principle. $(Takeh=6.63\times {10}^{-34}Js)$

• A. $1.05\times ,{10}^{-25}kgm{s}^{-1}$
• B. $2.03\times ,{10}^{-31}kgm{s}^{-1}$
• C. $3.05\times ,{10}^{-34}kgm{s}^{-1}$
• D. $2.49\times ,{10}^{-32}kgm{s}^{-1}$

Answer 1

Answer: (A)

$1.05\times ,{10}^{-25}kgm{s}^{-1}$

Here $\Delta x=1nm={10}^{-9}m$
By Heisenberg uncertainty principle, $\Delta x\Delta p=h$
$\therefore$ $\Delta p=\frac{h}{\Delta x}=\frac{h}{2\pi \Delta x}$ $[\because h=\frac{h}{2\pi }]$

$=\frac{6.63\times {10}^{-34}}{2\times \pi \times {10}^{-9}}=1.05\times {10}^{-25}kgm{s}^{-1}$

Option A