**Heisenberg's Uncertainty Principle **tries to explain the potential duality of an electron behaving as either a particle or wave.

Heisenberg's Uncertainty Principle illustrates that an electron can behave as a particle or as a wave, but never both simultaneously.

**Concept:** The duality of an electron.

**Concept:** To illustrate this dual nature of an electron Heisenberg created his Uncertainty or Indeterminacy Principle

**Example:** An electron has an uncertainty in its position of 630 pm. What is the uncertainty in its velocity?

A student is examining a bacterium under the microscope. The E. coli bacterial cell has a mass of = 0.500 (where a femtogram,fg , is 10^{-15} g) and is swimming at a velocity of v = 9.00 um/s, with an uncertainty in the velocity of 8.00 %. E. coli bacterial cells are around 1 um (10^{-6}m ) in length. The student is supposed to observe the bacterium and make a drawing. However, the student, having just learned about the Heisenberg uncertainty principle in physics class, complains that she cannot make the drawing. She claims that the uncertainty of the bacterium's position is greater than the microscope's viewing field, and the bacterium is thus impossible to locate.

What is the uncertainty of the position of the bacterium? Express your answer numerically in meters.

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According to the Heisenberg uncertainity principle , if the uncertainity in the speed of an electron is 3.5 x 10^{3} m/s, the uncertainity in its position (in m) is at least:

A) 66 m

B) 1.7 x 10^{-8} m

C) 17 m

D) 2.1 x 10^{-10} m

E) 6.6 x 10^{-8} m

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According to the Heisenberg uncertainty principle, if the uncertainty in the speed of an electron is 3.5 x 10^{3} m/s, the uncertainty in its position (in m) is at least (mass electron = 9.11 x 10^{-31} kg) __.

A) 1.7 x 10^{-8} m

B) 6.6 x 10^{-8} m

C) 17 m

D) 66 m

E) None of these choices is correct

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To what uncertainty (in m) can the position of a baseball traveling at 45.0 m/s be measured if the uncertainty of its speed is 0.10%? The mass of a baseball is about 0.145 kg.

a. 8.1 x 10^{-33} m

b. 5.6 x 10^{-15} m

c. 6.7 x 10^{-45} m

d. 5.9 x 10^{-14} m

e. 4.4 x 10^{-65} m

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An electron traveling at 3.7 x 10 ^{5} m/s has an uncertainty in its velocity of 1.88 x 10 ^{5} m/s. What is the uncertainty in its position.

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An electron has an uncertainty in its position of 552 pm. What is the uncertainty in its velocity?

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An alpha particle with mass = 6.6 x 10 ^{−24} g moves at a speed of 1.52 x 10 ^{7} ± 0.03 m/s. What is the minimum uncertainty of its position?

a) 2.66 x 10 ^{−10} m

b) 2.66 x 10 ^{−7} m

c) 6.54 x 10 ^{−3} m

d) 8.54 x 10 ^{−3} m

e) 1.75 x 12 ^{−5} m

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An electron has an uncertainty in its position of 190 pm. What is its uncertainty in its velocity?

- 272 x 10
^{3}m/s

- 1.12 x 10
^{5}m/s

- 521 x 10
^{5}m/s

- 4.21 x 10
^{2}m/s

- 305 x 10
^{3}m/s

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According to the Heisenberg uncertainty principle, if the uncertainty in the speed of an electron is 3.5 x 10^{3} m/s, the uncertainty in its position (in m) is at least.

- 66 m

- 17 m

- 6.6 x 10
^{-8}m

- 1.7 x 10
^{-8 }m

- 2.1 x 10
^{-10}m

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