Question

For an electron whose positional uncertainty is $1.0\times 10^{- 10} \, m$ , the uncertainty in the component of the velocity in m $s^{- 1}$ will be

• A. $5.8 \times 10^{5}$
• B. $10^{9}$
• C. $10^{2}$
• D. $10^{15}$

Answer 1

Answer: (A)

According to uncertainty principle
$\Rightarrow \delta x \times \delta p =\frac{ h }{4 \pi }$
$\Rightarrow \delta p =\frac{ h }{4 \pi \times \delta x }$
$\Rightarrow m \delta v =\frac{ h }{4 \pi \delta x }$
$\delta v=\frac{h}{4 \pi m \delta x}$
$=\frac{6.625 \times 10^{-34}}{9.1 \times 10^{-31} \times 10^{-10} \times 4 \times 3.14}=5.8 \times 10^{5}$