A student measures the position of an electron to within and claims that the…

CHEMISTRY · Subjective · CBSE · Chemistry · Structure of Atom · Structure of Atom

Problem

A student measures the position of an electron to within

\Delta x = 1.0\,\mu\text{m}

and claims that the uncertainty in its speed is only

\Delta v = 0.50\,\text{m s}^{-1}

. For an electron (mass

m_{\text{e}} = 9.11\times10^{-31}\,\text{kg}

) and

h = 6.63\times10^{-34}\,\text{J s}

: By what minimum factor must the quoted value of

\Delta v

be multiplied so that the position--momentum uncertainty relation is satisfied?