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
The uncertainty in position is equal to de Broglie wavelength. $\Delta x=\lambda=h / 4 \pi m \ldots \ldots$
The uncertainty in position is equal to de Broglie wavelength. $\Delta x=\lambda=h / 4 \pi m \ldots \ldots$
The Heisenberg's uncertainty principle is $\Delta x \Delta v>=h / 4 \pi m \ldots$ ( 2)
From equations (1) and (2), $(h / m v \times \Delta v>=h / 4 \pi m)$
Thus, $\Delta v / v>=14 \pi$
Hence, minimum percentage error $=\Delta v / v \times 100=100 / 4 \pi=8$
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