The Heisenberg Uncertainty Principle (7.1.7) Flashcards
• One locates things by detecting the photons that bounce off the object from a
light source.
• 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.
• 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.
One locates things by detecting the photons that
bounce off the object from a light source.
The wavelength (λ)of light used to view an object
must be smaller than the object viewed. For
example, radar (λ≈ 1 m) can be used to view a ship,
but visible light (λ ≈ 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
(λ ≈ 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
(λ ≈ 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 locate a cat with rubber balls—one might
locate the cat, but the momentum of the cat would
be changed in the act of finding the cat.
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 (∆ρ)
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.
One locates things by detecting the photons that
bounce off the object from a light source.
The wavelength (λ)of light used to view an object
must be smaller than the object viewed. For
example, radar (λ≈ 1 m) can be used to view a ship,
but visible light (λ ≈ 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
(λ ≈ 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
(λ ≈ 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 locate a cat with rubber balls—one might
locate the cat, but the momentum of the cat would
be changed in the act of finding the cat.
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 (∆ρ)
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.
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?
5.3 × 10^−10 m (A)
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.)
an electron with a measured velocity of 1.8 × 10^5 m / s, plus or minus 2% (A)
Which of the following changes would not affect the resolution of a light microscope?
increasing the intensity of the light (A)
Which of the following is a consequence of the Heisenberg uncertainty principle?
The exact path taken by an electron cannot be determined, only its probable path. (A)
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?
4.07 × 10^9 s^−1 (C)
Which of the following would be an advantage of using infrared light rather than ultraviolet light to observe electrons?
Infrared light has a lower energy per photon. (D)
Why is it possible to predict the momentum of a golf ball much more accurately than that of an electron?
The energy of the photons used to observe a golf ball is small compared to the energy of the golf ball. (C)
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)
7.1 × 10^−16 J (C)
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.
3000 (C)
Suppose two photons of light strike an electron, one after the other. What information could be learned from these collisions?
the electron’s position at the instant of the first collision (B)
