The speed of an electron is known to be between 60106 ms and

The speed of an electron is known to be between 6.0×106 m/s and 6.6×106 m/s . Estimate the uncertainty in its position.

Please show all work, equations and units!

Solution

uncertainity in speed of an electron is dv = (6.6-6)*10^6 = 0.6*10^6 m/sec

then according to uncertainity principle

dx*dp >= h/(4*pi)

uncertainity in position is dx > = h/(4*pi*m*dv)

dx > = (6.625*10^-34)/(4*3.142*9.11*10^-31*0.6*10^6)

dx > = 9.64*10^-11 m