Question

An electron is allowed to move freely in a closed cubic box of length of side $10cm$. The uncertainity in its velocity will be:

• A. $3.35\times {10}^{-3}m/sec$
• B. $5.8\times {10}^{-4}m/sec$
• C. $4\times {10}^{-5}m/sec$
• D. $4\times {10}^{-6}m/sec$

Answer 1

The correct option is A $3.35\times {10}^{-3}m/sec$

If $a$ is side of a cube, then $\Delta x=a\sqrt{3}$

$\therefore \Delta x=10\sqrt{3}cm=10\sqrt{3}\times {10}^{-3}m$

$\Delta x.\Delta p=\frac{h}{4\pi };\Delta x.m.\Delta v=\frac{h}{4\pi }$

$\Delta v=\frac{h}{4\pi m.\Delta x}$

$=\frac{6.63\times {10}^{-34}}{4\times 3.14\times 9.1\times {10}^{-31}\times 10\times \sqrt{3}\times {10}^{-3}}$

$\therefore △v\approx 3.34\times {10}^{-3}m{s}^{-1}$

Hence, the correct option is $A$