Question

The uncertainity in the position of an electron moving with a velocity of $3\times {10}^{4}cm/sec$ is accurate upto $0.011\%$ will be ?

• A. 1.92 cm
• B. 7.68 cm
• C. 1.75$\times$10${}^{-3}$ cm
• D. 3.84 cm

Answer 1

Answer: (C)

1.75$\times$10${}^{-3}$ cm

uncertainty in velocity $=3\times {10}^4\times \frac{0.011}{100}$

$=3\times {10}^4\times 11\times {10}^{-5}$

$=33\times {10}^{-1}$

$=3.3$

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

$\delta x=\frac{h}{4\pi m\Delta v}=\frac{6.626\times {10}^{-34}}{4\times 3.14\times 9.1\times {10}^{-31}\times 3.3}$

$=\frac{6.626\times {10}^{-34}}{377.18\times {10}^{-31}}$

$=0.01756\times {10}^{-34}\times {10}^{31}$

$0.0175\times {10}^{-3}$m

$\Delta x=1.75\times {10}^{-3}cm$

Hence, the correct option is $\text{C}$