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There is another consequence of the uncertainty principle for energy and time. If energy is uncertain by Δ E size 12{ΔE} {} , then conservation of energy can be violated by Δ E size 12{ΔE} {} for a time Δ t size 12{Δt} {} . Neither the physicist nor nature can tell that conservation of energy has been violated, if the violation is temporary and smaller than the uncertainty in energy. While this sounds innocuous enough, we shall see in later chapters that it allows the temporary creation of matter from nothing and has implications for how nature transmits forces over very small distances.

Finally, note that in the discussion of particles and waves, we have stated that individual measurements produce precise or particle-like results. A definite position is determined each time we observe an electron, for example. But repeated measurements produce a spread in values consistent with wave characteristics. The great theoretical physicist Richard Feynman (1918–1988) commented, “What there are, are particles.” When you observe enough of them, they distribute themselves as you would expect for a wave phenomenon. However, what there are as they travel we cannot tell because, when we do try to measure, we affect the traveling.

Section summary

  • Matter is found to have the same interference characteristics as any other wave.
  • There is now a probability distribution for the location of a particle rather than a definite position.
  • Another consequence of the wave character of all particles is the Heisenberg uncertainty principle, which limits the precision with which certain physical quantities can be known simultaneously. For position and momentum, the uncertainty principle is Δ x Δ p h size 12{ΔxΔp>= { {h} over {4π} } } {} , where Δ x size 12{Δx} {} is the uncertainty in position and Δ p size 12{Δp} {} is the uncertainty in momentum.
  • For energy and time, the uncertainty principle is Δ E Δ t h size 12{ΔEΔt>= { {h} over {4π} } } {} where Δ E size 12{ΔE} {} is the uncertainty in energy and Δ t size 12{Δt} {} is the uncertainty in time.
  • These small limits are fundamentally important on the quantum-mechanical scale.

Conceptual questions

What is the Heisenberg uncertainty principle? Does it place limits on what can be known?

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Problems&Exercises

(a) If the position of an electron in a membrane is measured to an accuracy of 1 . 00 μm size 12{1 "." "00 μm"} {} , what is the electron’s minimum uncertainty in velocity? (b) If the electron has this velocity, what is its kinetic energy in eV? (c) What are the implications of this energy, comparing it to typical molecular binding energies?

(a) 57.9 m/s

(b) 9 . 55 × 10 9 eV size 12{9 "." "55" times "10" rSup { size 8{ - 9} } " eV"} {}

(c) From [link] , we see that typical molecular binding energies range from about 1eV to 10 eV, therefore the result in part (b) is approximately 9 orders of magnitude smaller than typical molecular binding energies.

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(a) If the position of a chlorine ion in a membrane is measured to an accuracy of 1 . 00 μm size 12{1 "." "00 μm"} {} , what is its minimum uncertainty in velocity, given its mass is 5 . 86 × 10 26 kg size 12{5 "." "86" times "10" rSup { size 8{ - "26"} } " kg"} {} ? (b) If the ion has this velocity, what is its kinetic energy in eV, and how does this compare with typical molecular binding energies?

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Suppose the velocity of an electron in an atom is known to an accuracy of 2 . 0 × 10 3 m/s size 12{2 "." 0 times "10" rSup { size 8{3} } " m/s"} {} (reasonably accurate compared with orbital velocities). What is the electron’s minimum uncertainty in position, and how does this compare with the approximate 0.1-nm size of the atom?

29 nm,

290 times greater

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The velocity of a proton in an accelerator is known to an accuracy of 0.250% of the speed of light. (This could be small compared with its velocity.) What is the smallest possible uncertainty in its position?

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A relatively long-lived excited state of an atom has a lifetime of 3.00 ms. What is the minimum uncertainty in its energy?

1 . 10 × 10 13 eV size 12{1 "." "10" times "10" rSup { size 8{ - "13"} } " eV"} {}

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(a) The lifetime of a highly unstable nucleus is 10 20 s size 12{"10" rSup { size 8{ - "20"} } " s"} {} . What is the smallest uncertainty in its decay energy? (b) Compare this with the rest energy of an electron.

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The decay energy of a short-lived particle has an uncertainty of 1.0 MeV due to its short lifetime. What is the smallest lifetime it can have?

3 . 3 × 10 22 s size 12{3 "." 3 times "10" rSup { size 8{ - "22"} } " s"} {}

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The decay energy of a short-lived nuclear excited state has an uncertainty of 2.0 eV due to its short lifetime. What is the smallest lifetime it can have?

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What is the approximate uncertainty in the mass of a muon, as determined from its decay lifetime?

2.66 × 10 46 kg size 12{2 "." "66" times "10" rSup { size 8{ - "46"} } " kg"} {}

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Derive the approximate form of Heisenberg’s uncertainty principle for energy and time, Δ E Δ t h size 12{ΔE Δt approx h} {} , using the following arguments: Since the position of a particle is uncertain by Δ x λ size 12{Δx approx λ} {} , where λ size 12{λ} {} is the wavelength of the photon used to examine it, there is an uncertainty in the time the photon takes to traverse Δ x size 12{Δx} {} . Furthermore, the photon has an energy related to its wavelength, and it can transfer some or all of this energy to the object being examined. Thus the uncertainty in the energy of the object is also related to λ size 12{λ} {} . Find Δ t size 12{Δt} {} and Δ E size 12{ΔE} {} ; then multiply them to give the approximate uncertainty principle.

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Questions & Answers

what is equilibrium
Sade Reply
If a system is said to be under equilibrium whenever there is no force act upon it... And it remain in its initial stage..
soniya
What is conductivity
Saud Reply
It is the ease with which electrical charges or heat can be transmitted through a material or a solution.
Cffrrcvccgg
how to find magnitude and direction
Arjune Reply
how to caclculate for speed
Arjune
derivation of ohms law
Kazeem Reply
derivation of resistance
Kazeem
R=v/I where R=resistor, v=voltage, I=current
Kazeem
magnitude
Arjune
A puck is moving on an air hockey table. Relative to an x, y coordinate system at time t 0 s, the x components of the puck’s ini￾tial velocity and acceleration are v0x 1.0 m/s and ax 2.0 m/s2 . The y components of the puck’s initial velocity and acceleration are v0y 2.0 m/s and ay 2.0
Arjune
Electric current is the flow of electrons
Kelly Reply
is there really flow of electrons exist?
babar
Yes It exists
Cffrrcvccgg
explain plz how electrons flow
babar
if electron flows from where first come and end the first one
babar
an electron will flow accross a conductor because or when it posseses kinectic energy
Cffrrcvccgg
electron can not flow jist trasmit electrical energy
ghulam
free electrons of conductor
ankita
electric means the flow heat current.
Serah Reply
electric means the flow of heat current in a circuit.
Serah
What is electric
Manasseh Reply
electric means?
ghulam
electric means the flow of heat current in a circuit.
Serah
electric means the flow of electric current through conductor
Sade
the continuos flow of electrons in a circuit is called electric
ANUBHA
electric means charge
ghulam
electric means current
Sade
a boy cycles continuously through a distance of 1.0km in 5minutes. calculate his average speed in ms-1(meter per second). how do I solve this
Jenny Reply
speed = distance/time be sure to convert the km to m and minutes to seconds check my utube video "mathwithmrv speed"
PhysicswithMrV
d=1.0km÷1000=0.001 t=5×60=300s s=d\t s=0.001/300=0.0000033m\s
Serah
A puck is moving on an air hockey table. Relative to an x, y coordinate system at time t 0 s, the x components of the puck’s ini￾tial velocity and acceleration are v0x 1.0 m/s and ax 2.0 m/s2 . The y components of the puck’s initial velocity and acceleration are v0y 2.0 m/s and ay 2.0
Arjune
why we cannot use DC instead of AC in a transformer
kusshaf Reply
becuse the d .c cannot travel for long distance trnsmission
ghulam
what is physics
Chiwetalu Reply
branch of science which deals with matter energy and their relationship between them
ghulam
Life science
the
what is heat and temperature
Kazeem Reply
how does sound affect temperature
Clement Reply
sound is directly proportional to the temperature.
juny
how to solve wave question
Wisdom Reply
I would like to know how I am not at all smart when it comes to math. please explain so I can understand. sincerly
Emma
Just know d relationship btw 1)wave length 2)frequency and velocity
Talhatu
First of all, you are smart and you will get it👍🏽... v = f × wavelength see my youtube channel: "mathwithmrv" if you want to know how to rearrange equations using the balance method
PhysicswithMrV
nice self promotion though xD
Beatrax
thanks dear
Chuks
hi pls help me with this question A ball is projected vertically upwards from the top of a tower 60m high with a velocity of 30ms1.what is the maximum height above the ground level?how long does it take to reach the ground level?
mahmoud
what is scalar quantities
babatunde
scaler quantity are quanties that have only direction and no magnitude
Natsu
ice Point
babatunde
scalar quantity are quantities that have magnitude but no direction
Ehigiamusoe
please guys help, what is the difference between concave lens and convex lens
Vincent Reply
convex lens brings rays of light to a focus while concave diverges rays of light
Christian
for mmHg to kPa yes
Matthew
it depends on the size
Matthew Reply
please what is concave lens
Vincent
a lens which diverge the ray of light
rinzuala
concave diverges light
Matthew
thank you guys
Vincent
A diverging lens
Yusuf
What is isotope
Yusuf
each of two or more forms of the same element that contain equal numbers of protons but different numbers of neutrons in their nuclei, and hence differ in relative atomic mass but not in chemical properties; in particular, a radioactive form of an element. "some elements have only one stable isotope
Karthi
Practice Key Terms 6

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Source:  OpenStax, College physics. OpenStax CNX. Jul 27, 2015 Download for free at http://legacy.cnx.org/content/col11406/1.9
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