An accelerated electron has a speed of $5 \times 10^{6} \ m \ s^{-1}$ with an uncertainty of $0.02 \ \%$. The uncertainty in finding its location while in motion is $x \times 10^{-9} \ m$. The value of $x$ is $......$ (Nearest integer)
[Use mass of electron $= 9.1 \times 10^{-31} \ kg, h = 6.63 \times 10^{-34} \ J \ s, \pi = 3.14]$

The equation $\Delta x \cdot \Delta p \ge \frac{h}{4\pi}$ shows

If uncertainty in the position of an electron is zero,the uncertainty in its momentum would be

If the uncertainty in momentum of a particle is twice the uncertainty in its position,what will be the uncertainty in the position of the particle?

Uncertainty in the position of an electron (mass $= 9.1 \times 10^{-31} \ kg$) moving with a velocity $300 \ ms^{-1}$ accurate up to $0.001 \ \%$ will be $(h = 6.63 \times 10^{-34} \ J \cdot s)$.

Given below are two statements $:$
Statement $(I):$ It is impossible to specify simultaneously with arbitrary precision,both the linear momentum and the position of a particle.
Statement $(II) :$ If the uncertainty in the measurement of position and uncertainty in measurement of momentum are equal for an electron,then the uncertainty in the measurement of velocity is $\geq \sqrt{\frac{h}{4\pi}} \times \frac{1}{m}$ which simplifies to $\geq \frac{1}{2m} \sqrt{\frac{h}{\pi}}$. In the light of the above statements,choose the correct answer from the options given below $:$