7.1.7 The Heisenberg Uncertainty Principle

Question 1

The Heisenberg Uncertainty Principle

Answer 1

• One locates things by detecting the photons that bounce off the object from a light source.
• The Heisenberg uncertainty principle states that the smaller the object the greater the relative uncertainty in knowing both the position and the momentum of that object.

Question 2

note

Answer 2

• One locates things by detecting the photons that bounce off the object from a light source.
• The wavelength ( )of light used to view an object must be smaller than the object viewed. For example, radar (
  1 m) can be used to view a ship, but visible light (
  5 x 10^–7 m) must be used for greater detail. Higher resolution requires still shorter wavelengths. However, the shorter the wavelength, the higher the frequency, and therefore the higher the energy of each photon. Higher energy photons have a greater effect on the object viewed, and therefore can change the object as it is being viewed. For example, ultraviolet light (2 x 10^–7 m) provides still greater resolution, but can damage skin.
• Electrons are very small. To view an electron, one would have to use electromagnetic radiation with a very short wavelength, such as gamma rays (1 x 10^–11 m). But gamma rays have a high energy, and would therefore affect the momentum of the electrons being studied. This is analogous to trying to loc
• The Heisenberg uncertainty principle states that the smaller the object the greater the relative uncertainty in knowing both the exact position and the momentum of that object.
• Mathematically, the error in momentum ( ) multiplied by
  the error in location ( x) is greater than or equal to
  Planck’s constant (h) divided by four pi. This works out to
  a very small number, and therefore isn’t important for
  macroscopic objects. However, relative to the size of an
  electron, this number is large. Therefore, it is impossible to know both the location and momentum of an electron
  precisely.

Question 3

The momentum of a proton is measured as 2.2 × 10^−21 kg • m / s. Suppose there is a 0.75% uncertainty in knowing the momentum. The minimum error in knowing this proton’s position is about how many times greater than the diameter of the proton?
The diameter of a proton is approximately 1 × 10^−15 m.

Answer 3

3000

Question 4

For which of the following electrons will Δx, the minimum error in knowing its position, be the greatest? (An object’s momentum is equal to its mass multiplied by its velocity.)

Answer 4

an electron with a measured velocity of 1.8 × 10^5 m / s, plus or minus 2%

Question 5

Which of the following is a consequence of the Heisenberg uncertainty principle?

Answer 5

The exact path taken by an electron cannot be determined, only its probable path.

Question 6

What is the energy per photon of the lowest frequency of electromagnetic radiation that can be used to observe a gold atom with a diameter of 280 picometers? (1 picometer = 1 × 10^−12 meter)

Answer 6

7.1 × 10^−16 J

Question 7

Electrons are ejected from a sample of silver when ultraviolet light is shined on it. The momentum of the fastest electrons is measured as 6.63 × 10^−25 kg • m / s. If there is a 15% uncertainty in knowing the momentum, what is the minimum error in knowing the position of the electrons?

Answer 7

5.3 × 10^−10 m

Question 8

A baseball has a diameter of 7.38 cm. What is the lowest frequency of electromagnetic radiation that can be used to observe the baseball?

Answer 8

4.07 × 10^9 s−1

Question 9

Suppose two photons of light strike an electron, one after the other. What information could be learned from these collisions?

Answer 9

the electron’s position at the instant of the first collision

Question 10

Why is it possible to predict the momentum of a golf ball much more accurately than that of an electron?

Answer 10

The energy of the photons used to observe a golf ball is small compared to the energy of the golf ball.

Question 11

Which of the following would be an advantage of using infrared light rather than ultraviolet light to observe electrons?

Answer 11

Infrared light has a lower energy per photon.

Question 12

Which of the following changes would not affect the resolution of a light microscope?

Answer 12

increasing the intensity of the light