Question

An electron and a 0.0220 kg bullet each have a velocity of magnitude 490 m/s, accurate to within 0.0100%. Within what lower limit could we determine the position of each object along the direction of the velocity? (Give the lower limit for the electron in mm and that for the bullet in m

(b)

What If? Within what lower limit could we determine the position of each object along the direction of the velocity if the electron and the bullet were both relativistic, traveling at 0.350c measured with the same accuracy? (Give the lower limit for the electron in nm and that for the bullet in m )

Answer 1

(1) mass of electron;

mass of bullet ;

Solution:

(A) The uncertainity in velocity for electron and bullet is;

= v x (0.01%)

from Heisenberg uncertainity principle,

position for electron;

position for bullet;

from equation (1);

from equation (2);

........................................................................................................................

(B) The uncertainity in velocity for electron and bullet is;

= v x (0.01%)

from equation (1);

from equation (2);