**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 #1: The duality of an electron.

Concept #2: To illustrate this dual nature of an electron Heisenberg created his Uncertainty or Indeterminacy Principle

Example #1: An electron has an uncertainty in its position of 630 pm. What is the uncertainty in its velocity?

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

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.

According to the Heisenberg uncertainity principle , if the uncertainity in the speed of an electron is 3.5 x 103 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

According to the Heisenberg uncertainty principle, if the uncertainty in the speed of an electron is 3.5 x 103 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

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

What is the difference between stating "The electron is located at a particular point in space" and "There is a high probability that the electron is located at a particular point in space"?

Do the implications of the uncertainty principle become more or less important as
the mass of an object increases?

What paradox is at least partially solved by the uncertainty principle?

Calculate the uncertainty in the position of an electron moving at a speed of (3.00 0.01) 105 m/s.
(Take the mass of the electron m=9.10910-31kg.)

Calculate the uncertainty in the position of a neutron moving at the same speed. (Take the mass of the neutron m=1.67510-27kg.)

Why does the uncertainty principle make it impossible to predict a trajectory for the electron?

Using Heisenbergs uncertainty principle, calculate the uncertainty in the position of a 1.60 -mg mosquito moving at a speed of 1.50 m/s
if the speed is known to within 0.01m/s.

Using Heisenbergs uncertainty principle, calculate the uncertainty in the position of a proton moving at a speed of (
5.10
0.01) 104 m/s.
( Take the mass of a proton m=1.67310-27kg.)

Consider the discussion of radial probability functions in the "A Closer Look" box in Section 6.6 in the textbook.What is the difference between the probability density as a function of r and the radial probability function as a function of r?

As discussed in the A Closer Look box on "Measurement and the Uncertainty Principle," the essence of the uncertainty principle is that we cant make a measurement without disturbing the system that we are measuring.Why cant we measure the position of a subatomic particle without disturbing it?

In the television series Star Trek, the transporter beam is a device used to "beam down" people from the Starship Enterprise to another location, such as the surface of a planet. The writers of the show put a "Heisenberg compensator" into the transporter beam mechanism.Explain why such a compensator would be necessary to get around Heisenbergs uncertainty principle.

Why does the uncertainty principle make it impossible to predict a trajectory for the electron?a. Because you cannot know both the position and velocity of the electron simultaneously.b. Because you cannot know both the position and force acting on the electron simultaneously.c. Because you cannot know the velocity of the electron.d. Because you cannot know the force acting on the electron.e. Because you cannot know both the velocity and force acting on the electron simultaneously.f. Because you cannot know the position of the electron.

Using Heisenberg’s uncertainty principle, calculate the uncertainty in the position of (a) a 1.50-mg mosquito moving at a speed of 1.40 m/s if the speed is known to within ∓0.01 m/s

Using Heisenberg’s uncertainty principle, calculate the uncertainty in the position of (b) a proton moving at a speed of (5.00 ∓ 0.01) x 104 m/s.

Calculate the uncertainty in the position of (a) an electron moving at a speed of (3.00 ∓ 0.01) x 105 m/s

Calculate the uncertainty in the position of (b) a neutron moving at this same speed. (The masses of an electron and a neutron are given in the table of fundamental constants)

Calculate the uncertainty in the position of (a) an electron moving at a speed of (3.00 ∓ 0.01) x 105 m/s, (b) a neutron moving at this same speed. (The masses of an electron and a neutron are given in the table of fundamental constants in the inside cover of the text.) (c)What are the implications of these calculations to our model of the atom?

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

Using the Heisenberg uncertainty principle, calculate Δx for a baseball (mass = 145 g) with Δν = 0.100 m/s. How does the answer correspond to the size of a baseball?

The Heisenberg uncertainty principle can be expressed in the form:where E represents energy and t represents time. Show that the units for this form are the same as the units for the form:

The 2005 Nobel Prize in Physics was given, in part, to scientists who had made ultrashort pulses of light. These pulses are important in making measurements involving very short time periods. One challenge in making such pulses is the uncertainty principle, which can be stated with respect to energy and time as ΔE • Δt ≥ h/4π. What is the wavelength of the high-energy end of the pulse that is limited only by the uncertainty principle?

State the Heisenberg uncertainty principle. Describe briefly what the principle implies.

Explain Heisenberg's uncertainty principle.

Calculate the uncertainty in the position of an electron and a neutron moving at a speed of (3.00 ± 0.01) x 105 m/s. Based on your answers, which can we know with greater precision,
the position of the electron or of the neutron?

An electron has an uncertainty in its position of 551 pm. What is the uncertainty in its velocity?

An electron traveling at 4.2×105 m/s has an uncertainty in its velocity of 1.51×105 m/s. What is the uncertainty in its position?

A 232-lb fullback runs 40 yd at 19.8 ± 0.1 mi/h. What is the uncertainty in his position?

An alpha particle (mass = 6.6 x 10 −24 g) emitted by a radium isotope travels at 3.4 x 107 ± 0.1 x 10 7 mi/h. What is the uncertainty in its position?

Using the Heisenberg uncertainty principle, calculate Δx for an electron with Δν = 0.100 m/s. How does the answer compare with the size of a hydrogen atom?

An electron has an uncertainty in its position of 552 pm. What is minimum possible value for the uncertainty in its velocity?a. 1.05 x 105 m/sb. 1.46 x 106 m/sc. 3.40 x 106 m/sd. 8.87 x 106 m/se. 2.21 x 107 m/s

According to the Heisenberg uncertainty principle, if the uncertainty in the speed of an electron is 3.5 x 103 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

An electron has an uncertainty in its position of 190 pm. What is its uncertainty in its velocity?272 x 103 m/s 1.12 x 105 m/s 521 x 105 m/s 4.21 x 102 m/s 305 x 103 m/s

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 (10-6m ) 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.

The 2005 Nobel Prize in Physics was given, in part, to scientists who had made ultrashort pulses of light. These pulses are important in making measurements involving very short time periods. One challenge in making such pulses is the uncertainty principle, which can be stated with respect to energy and time as ΔE • Δt ≥ h/4πlarge{Delta EcdotDelta t ge frac{
m h}{4pi}}. What is the energy uncertainty (ΔE) associated with a short pulse of laser light that lasts for only 5.1 femtoseconds (fs)? Suppose the low-energy end of the pulse had a wavelength of 713 nm.

Which of the following statements is FALSE? A) Part of the Bohr model proposed that electrons in the hydrogen atom are located in "stationary states" or particular orbits around the nucleus. B) An orbital is the volume in which we are most likely to find an electron. C) The Heisenberg uncertainty principle implies that we can never know both the exact location and speed of an electron. D) The emission spectrum of a particular element is always the same and can be used to identify that element. E) Light has properties of both waves and particles, but electrons never behave like waves.