Question

The uncertainty in the position of an electron ( mass $=9.1\times {10}^{-28}g$) moving with a velocity of $3.0\times {10}^{4}cm{s}^{-1}$ accurate upto 0.001% will be

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

Answer 1

The correct option is A 1.92 cm

$△p=m\times △v$
$△p=9.1\times {10}^{-28}\times 3.0\times {10}^4\times \frac{0.001}{100}$
$△p=2.73\times {10}^{-28}$
Hence, $△x=\frac{h}{△p\times 4\pi }=\frac{6.626\times {10}^{-27}}{2.73\times {10}^{-28}\times 4\times 3.14}$
$△x=1.92cm$