Question

Uncertainty in the position of an electron $(mass=9.1\times {10}^{-31}kg)$ moving with a velocity $300m{s}^{-1}$ accurate upon 0.001% will be:

$[h=6.63\times {10}^{-34}J-s]$

• A. $19.2\times {10}^{-2}m$
• B. $5.76\times {10}^{-2}m$
• C. $1.92\times {10}^{-2}m$
• D. $3.84\times {10}^{-2}m$

Answer 1

The correct option is C $1.92\times {10}^{-2}m$

According to Heisenberg's uncertainity principle

$\Delta x\times m\times \Delta V=\frac{h}{4\pi }$

$\Delta x=$ uncertainty in the position

$m=9.1\times {10}^{-31}kg=$ mass of electron

$\Delta V=300\times \frac{0.001}{100}=0.003m/s$

uncertainty in the velocity

$h=6.62\times {10}^{-36}Js=$ Planck's constant

Substitute values in the above formula

$\Delta x\times 9.1\times {10}^{-31}\times 0.003=\frac{6.62\times {10}^{-34}}{4\times 3.1416}$

$\Delta x=1.92\times {10}^{-2}m$

Hence, the correct option is $C$