MCQ
The uncertainity in the location of circulating electron is equal in it's de-Broglie wavelength the minimum percent error in it's measurement of velocity under this cicumstances will be approximately
  • A
    $4$
  • $8$
  • C
    $18$
  • D
    $22$

Answer

Correct option: B.
$8$
b
$\Delta x=\lambda$

$\Delta \mathrm{x} \times \Delta \mathrm{V}=\frac{\mathrm{h}}{4 \pi \mathrm{m}}$

$\lambda \times \Delta \mathrm{V}=\frac{\mathrm{h}}{4 \pi \mathrm{m}}$

$\frac{\mathrm{h}}{\mathrm{mv}} \times \Delta \mathrm{V}=\frac{\mathrm{h}}{4 \pi \mathrm{m}}$

$\frac{\Delta V}{V} \%=\frac{1}{4 \pi} \times 100=8$

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