Question

The position and momentum of 1 keV electron are simultaneously measured. If the
uncertainty in its position is 1Å, calculate the uncertainty in its momentum. Mass of
electron = 9.1 10−31kg

Answer 1

Answer on question # 51440, Physics, Solid State Physics

Question The position and momentum of 1 keV electron are simultaneously measured. If the uncertainty in its position is 1A, calculate the uncertainty in its momentum. Mass of electron = $9.1\cdot 10^{-31}$kg ?

Solution Uncertainty principle tells us

$\delta x\cdot\delta p_{x}\geq\frac{\hbar}{2}$

where $\hbar\approx 1.05\cdot 10^{-34}$ $J\cdot s$ Hence, knowing $\delta x$ we can find $\delta p_{x}$:

$\delta p_{x}=\frac{\hbar}{2\delta x}=\frac{1.05\cdot 10^{-34}}{2\cdot 10^{-10}}\approx 5\cdot 10^{-23}\,m\cdot s$

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