Question

Uncertainty in position of an electron $(mass=9.1\times {10}^{-28g})$ moving with a velocity of $3\times {10}^4$ cm/s accurate upto 0.001% will be: $(Useh/4\pi$ in uncertainty expression where h = $6.626\times {10}^{-27}erg-s)$

• A. 5.76 cm
• B. 7.68 cm
• C. 1.93 cm
• D. 3.84 cm

Answer 1

Answer: (C)

1.93 cm

man of electron $m_e=9.1\times {10}^{31}$

uncertainity in velocity=$△v=\frac{v\times 0.001}{100}$

$=3\times {10}^4\times 1\times {10}^{-5}$

$=3\times {10}^{-1}$

uncertainity in Momentum$=△P=m_e△v$

$=3\times {10}^{-1}\times 9.1\times {10}^{-31}\times {10}^3$

$=2.73\times {10}^{-31}\times {10}^3$

$=2.73\times {10}^{-28}gc{m}^{-1}$

$=△P.△x\ge \frac{4}{\pi }$

$=△x\ge \frac{h}{4\pi \times 2.73\times {10}^{-28}}$

$=\frac{6.626\times {10}^{-27}}{4\pi \times 2.73\times {10}^{-28}}$

$=1.93cm$