The uncertainty in velocity is #Deltav = 1.05 * 10^(5) "m/s"#.
According to the Heisenberg Uncertainty Principle, you cannot measure simultaneously with great precision both the momentum and the position of a particle.
Mathematically, this is expressed as
#Deltap * Deltax>= h/(4pi)#, where
#Deltap# - the uncertainty in momentum;
#Deltax# - the uncertainty in position;
#h# - Planck's constant - #6.626 * 10^(-34)"m"^2"kg s"^(-1)#
The uncertainty in velocity can be calculated from the uncertainty in momentum by
#Deltap = m * Deltav => Deltav = (Deltap)/m#, where
#m# - the mass of an electron - #9.10938 * 10^(-31)"kg"#.
So, the first thing to do is figure out the uncertainty in momentum
#Deltap >= h/(4pi) * 1/(Deltax)#
#Deltap >= (6.626 * 10^(-34)"m"^(cancel(2))"kg s"^(-1))/(4 * pi * 553 * 10^(-12)cancel("m")) >= 9.5349 * 10^(-26)"m kg s"^(-1)#
This means that the uncertainty in velocity will be
#Deltav = (9.5349 * 10^(-26)cancel("kg")"m s"^(-1))/(9.10938 * 10^(-31)cancel("kg")) = 1.0467 * 10^(5)"m s"^(-1)#
Rounded to three sig figs, the number of sig figs given for 553 pm, the answer will be
#Deltav = color(green)(1.05 * 10^(5)"m s"^(-1))#
