Question

The uncertainly in the location of circulating electron is equal to its de-Broglie wavelength. Find the minimum percent error in its measurement of velocity under this circumstance.

Answer 1

The uncertainty in position is equal to de Broglie wavelength.

$\Delta x=\lambda =h/4\pi m$.......(1)

The Heisenberg's uncertainty principle is $\Delta x\Delta v>=h/4\pi m$......(2)

From equations (1) and (2),

$(h/mv\times \Delta v>=h/4\pi m)$

Thus, $\Delta v/v>=14\pi$

Hence, minimum percentage error $=\Delta v/v\times 100=100/4\pi =8$