Question

The uncertainty in position of an electron $(m=9.1\times {10}^{-28}gm)$ moving with a velocity $3\times {10}^4$ cm/s accurate upto 0.001% will be:

• A. 3.84 cm
• B. 1.92 cm
• C. 7.68 cm
• D. 5.76 cm

Answer 1

Answer: (B)

1.92 cm

Velocity is $3\times {10}^{4}cm{s}^{-1}=300m{s}^{-1}$

The velocity is "accurate up to 0.001%".

It indicates that the uncertainty in velocity is 0.001% of actual value, 300 m s^{-1}.

i.e.

uncertainty in velocity $\left(\Delta v\right)=300\times 0.001/100=3\times 10-3m{s}^{-1}$

$\Delta v=0.3$

From uncertainty principle-

$\Delta x\times \Delta p\ge \frac{h}{4\pi }$

$\Delta x=\frac{h}{4\pi m\Delta v}=\frac{6.6\times {10}^{-27}}{4\times 3.14\times 9.1\times {10}^{-28}\times 0.3}=1.92\times {10}^{-2}m=1.92cm$.

Hence, the correct option is B.