The uncertainty of velocity of an electron is $5.7 \times 10^5 \ m \ s^{-1}$. Find its uncertainty in position.

Based on Heisenberg's uncertainty principle,the uncertainty in the velocity of the electron to be found within an atomic nucleus of diameter $10^{-15} \ m$ is ............. $\times 10^9 \ ms^{-1}$ (nearest integer)
[Given : mass of electron $= 9.1 \times 10^{-31} \ kg$,Plank's constant $(h) = 6.626 \times 10^{-34} \ Js$ ]
(Value of $\pi = 3.14$ )

The uncertainty in the position of an electron and a helium atom is the same. If the uncertainty in the momentum of the electron is $32 \times 10^5$,then the uncertainty in the momentum of the helium atom is:

The uncertainty in the position of an electron moving with a velocity of $3 \times 10^4 \ cm/s$ is (given mass of electron $= 9.1 \times 10^{-28} \ g$,uncertainty in velocity $= 0.02 \ \%$).

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 $:$

Uncertainty in position of a $0.25 \ g$ particle is $10^{-5} \ m$. What is the uncertainty in its velocity? (Given: $h = 6.6 \times 10^{-34} \ J \ s$)