Question

An accelerated electron has a speed of $5\times {10}^{6}m{s}^{-1}$ with an uncertainty of 0.02%. The uncertainty in finding its location while in motion is $x\times {10}^{-9}m$. The value of x is .
[Use mass of electron $=9.1\times {10}^{-31}kg,h=6.63\times {10}^{-34}Js,\pi 3.14$]

Answer 1

Uncertainty in speed of electron $=\frac{0.02}{100}\times 5\times {10}^6$
$={10}^{3}m{s}^{-1}$
$m\Delta v\times \Delta x=\frac{h}{4\pi }$

$\Delta x=\frac{6.63\times {10}^{-34}}{4\times 3.14\times 9.1\times {10}^{-31}\times {10}^3}$

$=5.80\times {10}^{-8}m=58.00\times {10}^{-9}m$
Value of X =58