An accelerated electron has


An accelerated electron has a speed of $5 \times 10^{6} \mathrm{~ms}^{-1}$ with an uncertainty of $0.02 \%$. The uncertainty in finding its location while in motion is $\times \times 10^{-9} \mathrm{~m}$. The value of $x$ is ____________(Nearest integer)

[Use mass of electron $=9.1 \times 10^{-31} \mathrm{~kg}$,$\left.\mathrm{h}=6.63 \times 10^{-34} \mathrm{Js}, \pi=3.14\right]$


$\Delta \mathrm{v}=\frac{0.02}{100} \times 5 \times 10^{6}=10^{3} \mathrm{~m} / \mathrm{s}$

$\Delta \mathrm{x} . \Delta \mathrm{v}=\frac{\mathrm{h}}{4 \pi \mathrm{m}}$

$\mathrm{x} \times 10^{-9} \times 10^{3}=\frac{6.63 \times 10^{-34}}{4 \times 3.14 \times 9.1 \times 10^{-31}}$

$\mathrm{x} \times 10^{-9} \times 10^{3}=0.058 \times 10^{-3}$

$\mathrm{x}=\frac{0.058 \times 10^{-6}}{10^{-9}}=58$

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