Question

In an atom, an electron is moving with a speed of $600m/s$ with an accuracy of $0.005\%$. Certainty with which the position of the electron can be located is:

($h=6.6\times {10}^{-34}kg{m}^2{s}^{-1}$ mass of elecrtron $m_e=9.1\times {10}^{-31}kg$)

• A. $5.10\times {10}^{-3}m$
• B. $1.92\times {10}^{-3}m$
• C. $3.84\times {10}^{-3}m$
• D. $1.52\times {10}^{-3}m$

Answer 1

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

u=$600mse{c}^{-1}$

$\therefore \Delta u=600\times \frac{100}{0.005}$

$\Rightarrow 0.30mse{c}^{-1}$

Now,$\Delta x.m.\Delta u=\frac{h}{4\pi }$

$\Delta x=\frac{6.6\times {10}^{-34}}{4\times 3.14\times 9.1\times {10}^{-31}\times 0.30}$

$\Rightarrow 1.92\times {10}^{-3}m$

Conclusion : Hence (B) is the correct answer