Question

What will be the uncertainty in velocity of an electron when the uncertainty in its position is $1000 \,\mathring{A} $?

• A. $5.79 \times 10^2\, m\,s^{-1}$
• B. $5.79 \times 10^8\, m\,s^{-1}$
• C. $5.79 \times 10^4\, m\,s^{-1}$
• D. $5.79 \times 10^{-10}\, m\,s^{-1}$

Answer 1

Answer: (A)

$\Delta x \cdot m\Delta v=\frac{h}{4\pi}$
$\Delta x=100\,\mathring{A} =1000\times10^{-10}\,m$ or $10^{-7}\,m$
$\Delta v=\frac{6.626 \times 10^{-34}\,J\,s}{4 \times3.14 \times9.1 \times 10^{-31} \,kg \times 10^{-7}\,m}$
$=5.79\times10^{2}\,m/s$