Question

Uncertainty in the position of an electron (mass =9.1 * 10^-31 kg) moving with a velocity 300 ms^-1 , accurate upto 0.001%, will be

Answer 1

the answer should be 1.91um
by putting this formula,x.p=h/4π

Answer 2

Given that,

Velocity of an electron, v = 300 m/s

Accuracy in the velocity of electron is 0.001 %

To find, Uncertainty in position of electron

Solution,

The Heisenberg uncertainty principle gives the relation between the uncertainty in position and velocity as :

$\Delta x{\cdot} \Delta p\ge \dfrac{h}{4\pi}$

Accuracy in the velocity of electron is 0.001 % so, $\Delta v=\dfrac{300\times 0.001}{100}=0.003\ m/s$

So,

$\Delta x = \dfrac{h}{4\pi m\Delta v}$

m is mass of electron and h is Planck's constant

$\Delta x= \dfrac{6.63\times 10^{-34}}{4\pi \times 9.1\times 10^{-31}\times 0.003}\\\\\Delta x=0.0193\ m$

So, the uncertainty in position of the electron is 0.0193 m.

Learn more,

Uncertainty principal

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