## German physicist Werner Heisenberg related the uncertainty of an object’s position ( Δ x ) to the uncertainty in its velocity ( Δ v ) Δ x ≥

Question

German physicist Werner Heisenberg related the uncertainty of an object’s position ( Δ x ) to the uncertainty in its velocity ( Δ v ) Δ x ≥ h 4 π m Δ v where h is Planck’s constant and m is the mass of the object. The mass of an electron is 9.11 × 10 − 31 kg. What is the uncertainty in the position of an electron moving at 1.00 × 10 6 m/s with an uncertainty of Δ v = 0.01 × 10 6 m/s ?

in progress 0
3 years 2021-08-03T10:31:55+00:00 1 Answers 7 views 0

The uncertainty in the position of the electron is

Explanation:

The Heisenberg uncertainty principle is defined as:

(1)

Where is the uncertainty in momentum, is the uncertainty in position and h is the Planck’s constant.

The momentum is defined as:

(2)

Therefore, equation 2 can be replaced in equation 1

Since, the mass of the electron is constant, v will be the one with an associated uncertainty.

(3)

Then, can be isolated from equation 3

(4)

But

Hence, the uncertainty in the position of the electron is