Question #5e7e8

1 Answer
Nov 22, 2017

#Δv>=2.895*10^5# (m/s)

Explanation:

Werner Karl Heisenberg found the uncertaintry principle in 1927.
The formula is #color(red)(ΔxΔp>=ħ/2)#, where
#Δx#: uncertainty of place
#Δp#: uncertainty of momentum
#ħ#: Dirac's constant (#ħ=h/(2pi)=1.055*10^-34" "(J*s)#

Let #m# the mass of electron and #Δv# the uncertainty of speed.
(#m=9.109*10^-31 kg#).

#Δp=mΔv#
#mΔxΔv>=ħ/2#
#Δv>=ħ/(2mΔx)#
#=(1.055*10^-34" "(J*s))/(2*9.109*10^-31 (kg) * 2.00*10^-10 (m))#
#=2.895*10^5# (m/s).

This may seem so large. However, it is only about one-thousandth of the speed of light(#c=2.99*10^8# m/s).