MCQ
The minimum uncertainty in the speed of an electron in an one dimensional region of length $2 a _{ o }$

(Where $a _{0}=$ Bohr radius $52.9 pm$ ) is $km s ^{-1}$

(Given : Mass of electron $=9.1 \times 10^{-31} kg$, Planck's constant $h =6.63 \times 10^{-34} \;Js$ )

  • $548$
  • B
    $547$
  • C
    $546$
  • D
    $545$

Answer

Correct option: A.
$548$
a
Heisenberg's uncertainty principle

$\Delta x \times \Delta p _{ x } \geq \frac{ h }{4 \pi}$

$\Rightarrow 2 a _{0} \times m \Delta v _{ r }=\frac{ h }{4 \pi}(\text { minimum })$

$\Rightarrow \Delta v _{ x}=\frac{ h }{4 \pi} \times \frac{1}{2 a _{0}} \times \frac{1}{ m }$

$=\frac{6.63 \times 10^{-34}}{4 \times 3.14 \times 2 \times 52.9 \times 10^{-12} \times 9.1 \times 10^{-31}}$

$=548273\; ms ^{-1}$

$=548.273\; km\;s ^{-1}$

$=548\; km\; s ^{-1}$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free