Question

A proton has momentum 10^-20 N.s and the uncertainty in the position of the proton is 10^-10 m. What is the minimum fractional uncertainty in the momentum of this proton?

Answer 1

Answer:

According to Heisenberg's uncertainty principle,

ΔxΔp≥

4π

h

Where Δx&Δp are the uncertainty in position and momentum respectively and h is Planck’s Constant.

Now, the uncertainty in position here is simply the region where your electron is confined. Here, it is 10

−10

∴Δp≥

4π×Δx

h

⇒Δp≥

4×3.14×10

−10

6.63×10

−34

⇒Δp≥5.27×10

−25

gms

−1

Hence, the uncertainty in the momentum is 5.27×10

−25

gms

−1