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

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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 ?

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Physics
3 years
2021-08-03T10:31:55+00:00
2021-08-03T10:31:55+00:00 1 Answers
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## Answers ( )

Answer: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