Question

In an atom, an electron is moving with a speed of $600m/s$ with an accuracy of $0.005\%$, certainity with which the position of the electron can be located is: $(h=6.6\times {10}^{-34}$ kg $m^2{s}^{-1}$, mass of electron $e_m=9.1\times {10}^{-31}$ kg)

• A. $1.52\times {10}^{-4}m$
• B. $5.01\times {10}^{-3}m$
• C. $1.92\times {10}^{-3}m$
• D. $3.84\times {10}^{-3}m$

Answer 1

The correct option is C $1.92\times {10}^{-3}m$

$\text{Step 1: Heisenberg's uncertainty prinicple}$

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

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

$\Delta x\ge \frac{h}{4\pi m\Delta v}$ $....\left(1\right)$

$\text{Step 2: Certainity in the Position of electron}\left(\Delta x\right)$

Here,$\Delta v=0.005\%$ of $600m/s$$=\frac{0.005}{100}\times 600$$=0.03m/s$

Put all values in $\left(1\right)$

$\Delta x\ge \frac{6.6\times {10}^{-34}Js}{4\times 3.14\times 9.1\times {10}^{-31}kg\times 0.03m/s}$

$\Delta x\ge 1.9248\times {10}^{-3}m$

Hence, Option (C) is correct