Question

If the mass of electron is $9.11\times {10}^{-31}$ kg. Planck's constant is $6.626\times {10}^{-34}$ J-s and uncertainty in position is $0.1\stackrel{o}{A}$, then uncertainty in velocity is?

• A. $5.79\times {10}^8$ m/s
• B. $5.79\times {10}^5$ m/s
• C. $5.79\times {10}^6$ m/s
• D. $5.79\times {10}^7$ m/s

Answer 1

The correct option is C $5.79\times {10}^6$ m/s

According to Heisenberg's uncertainty principle,

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

$\Delta x=0.1A^0$, $m=9.11\times {10}^{-31}kg$

$\Delta v=\frac{6.626\times {10}^{-34}J-s}{4\pi \times 9.11\times {10}^{-31}kg\times {10}^{-11}m}$

$\Delta v=5.79\times {10}^{6}m/s$