Question

A beam of electrons with momentum p=10^-23 kg m/s passed through a narrow slit of width d=10^-5 m. What is the uncertainty component of the momentum in the x-direction due to the uncertainty principle (approximately)?
a. change in p greater or equal to 10^-26 kg m/s
b. change in p greater or equal to 10^-29 kg m/s
c. change in p greater or equal to 10^-32 kg m/s
d. change in p greater or equal to 10^-35 kg m/s

What is the uncertainty component of the velocity in the x-direction?
a. change in v greater or equal to 10^4 m/s
b. change in v greater or equal to 10 m/s
c. change in v greater or equal to 10^-2 m/s
d. change in v greater or equal to 10^-5 m/s
My answers do not match the choices. Please show the solution. Thanks.

Answer 1

Δp•Δx≥h
Δx=d=10⁻⁵
Δp•d ≥h
Δp≥h/d=6.63•10⁻³⁴/10⁻⁵=6.63•10⁻²⁹
b. change in p greater or equal to 10^-29 kg m/s

mΔv•Δx≥h
Δx=d =
m =10⁻³º
Δv ≥ h/m• Δx=10⁻⁵
=6.63•10⁻³⁴/10⁻³º•10⁻⁵ ∼10
b. change in v greater or equal to 10 m/s