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Why don’t we notice Heisenberg’s uncertainty principle in everyday life? The answer is that Planck’s constant is very small. Thus the lower limit in the uncertainty of measuring the position and momentum of large objects is negligible. We can detect sunlight reflected from Jupiter and follow the planet in its orbit around the Sun. The reflected sunlight alters the momentum of Jupiter and creates an uncertainty in its momentum, but this is totally negligible compared with Jupiter’s huge momentum. The correspondence principle tells us that the predictions of quantum mechanics become indistinguishable from classical physics for large objects, which is the case here.

Heisenberg uncertainty for energy and time

There is another form of Heisenberg’s uncertainty principle     for simultaneous measurements of energy and time . In equation form,

Δ E Δ t h , size 12{ΔE Δt>= { {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    . This means that within a time interval Δ t size 12{Δt} {} , it is not possible to measure energy precisely—there will be an uncertainty Δ E size 12{ΔE} {} in the measurement. In order to measure energy more precisely (to make Δ E size 12{ΔE} {} smaller), we must increase Δ t size 12{Δt} {} . This time interval may be the amount of time we take to make the measurement, or it could be the amount of time a particular state exists, as in the next [link] .

Heisenberg uncertainty principle for energy and time for an atom

An atom in an excited state temporarily stores energy. If the lifetime of this excited state is measured to be 1.0×10 10 s size 12{"10" rSup { size 8{ - "10"} } `s} {} , what is the minimum uncertainty in the energy of the state in eV?


The minimum uncertainty in energy Δ E size 12{ΔE} {} is found by using the equals sign in Δ E Δ t h /4 π size 12{ΔE Δt>= h"/4"π} {} and corresponds to a reasonable choice for the uncertainty in time. The largest the uncertainty in time can be is the full lifetime of the excited state, or Δ t = 1.0×10 10 s size 12{Δt="10" rSup { size 8{ - "10"} } `s} {} .


Solving the uncertainty principle for Δ E size 12{ΔE} {} and substituting known values gives

Δ E = h 4πΔt = 6 . 63 × 10 –34 J s ( 1.0×10 –10 s ) = 5 . 3 × 10 –25 J. size 12{ΔE= { {h} over {4πΔt} } = { {6 "." "63 " times " 10" rSup { size 8{"–34"} } " J " cdot " s"} over {4π \( "10" rSup { size 8{"–10"} } " s" \) } } =" 5" "." "3 " times " 10" rSup { size 8{"–25"} } " J" "." } {}

Now converting to eV yields

Δ E = (5.3 × 10 –25 J) ( 1 eV 1 . 6 × 10 –19 J ) = 3 . 3 × 10 –6 eV . size 12{ΔE =" 5" "." "3 " times " 10" rSup { size 8{"–25"} } " J " cdot { {"1 eV"} over {1 "." "6 " times " 10" rSup { size 8{"–19"} } " J"} } =" 3" "." "3 " times " 10" rSup { size 8{"–6"} } " eV" "." } {}


The lifetime of 10 10 s size 12{"10" rSup { size 8{ - "10"} } `s} {} is typical of excited states in atoms—on human time scales, they quickly emit their stored energy. An uncertainty in energy of only a few millionths of an eV results. This uncertainty is small compared with typical excitation energies in atoms, which are on the order of 1 eV. So here the uncertainty principle limits the accuracy with which we can measure the lifetime and energy of such states, but not very significantly.

The uncertainty principle for energy and time can be of great significance if the lifetime of a system is very short. Then Δ t size 12{Δt} {} is very small, and Δ E size 12{ΔE} {} is consequently very large. Some nuclei and exotic particles have extremely short lifetimes (as small as 10 25 s size 12{"10" rSup { size 8{ - "25"} } `s} {} ), causing uncertainties in energy as great as many GeV ( 10 9 eV size 12{"10" rSup { size 8{9} } `"eV"} {} ). Stored energy appears as increased rest mass, and so this means that there is significant uncertainty in the rest mass of short-lived particles. When measured repeatedly, a spread of masses or decay energies are obtained. The spread is Δ E size 12{ΔE} {} . You might ask whether this uncertainty in energy could be avoided by not measuring the lifetime. The answer is no. Nature knows the lifetime, and so its brevity affects the energy of the particle. This is so well established experimentally that the uncertainty in decay energy is used to calculate the lifetime of short-lived states. Some nuclei and particles are so short-lived that it is difficult to measure their lifetime. But if their decay energy can be measured, its spread is Δ E size 12{ΔE} {} , and this is used in the uncertainty principle ( Δ E Δ t h /4 π ) to calculate the lifetime Δ t size 12{Δt} {} .

Questions & Answers

Is there any normative that regulates the use of silver nanoparticles?
Damian Reply
what king of growth are you checking .?
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
Stoney Reply
why we need to study biomolecules, molecular biology in nanotechnology?
Adin Reply
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
what school?
biomolecules are e building blocks of every organics and inorganic materials.
anyone know any internet site where one can find nanotechnology papers?
Damian Reply
sciencedirect big data base
Introduction about quantum dots in nanotechnology
Praveena Reply
what does nano mean?
Anassong Reply
nano basically means 10^(-9). nanometer is a unit to measure length.
do you think it's worthwhile in the long term to study the effects and possibilities of nanotechnology on viral treatment?
Damian Reply
absolutely yes
how to know photocatalytic properties of tio2 nanoparticles...what to do now
Akash Reply
it is a goid question and i want to know the answer as well
characteristics of micro business
for teaching engĺish at school how nano technology help us
Do somebody tell me a best nano engineering book for beginners?
s. Reply
there is no specific books for beginners but there is book called principle of nanotechnology
what is fullerene does it is used to make bukky balls
Devang Reply
are you nano engineer ?
fullerene is a bucky ball aka Carbon 60 molecule. It was name by the architect Fuller. He design the geodesic dome. it resembles a soccer ball.
what is the actual application of fullerenes nowadays?
That is a great question Damian. best way to answer that question is to Google it. there are hundreds of applications for buck minister fullerenes, from medical to aerospace. you can also find plenty of research papers that will give you great detail on the potential applications of fullerenes.
what is the Synthesis, properties,and applications of carbon nano chemistry
Abhijith Reply
Mostly, they use nano carbon for electronics and for materials to be strengthened.
is Bucky paper clear?
carbon nanotubes has various application in fuel cells membrane, current research on cancer drug,and in electronics MEMS and NEMS etc
so some one know about replacing silicon atom with phosphorous in semiconductors device?
s. Reply
Yeah, it is a pain to say the least. You basically have to heat the substarte up to around 1000 degrees celcius then pass phosphene gas over top of it, which is explosive and toxic by the way, under very low pressure.
Do you know which machine is used to that process?
how to fabricate graphene ink ?
for screen printed electrodes ?
What is lattice structure?
s. Reply
of graphene you mean?
or in general
in general
Graphene has a hexagonal structure
On having this app for quite a bit time, Haven't realised there's a chat room in it.
what is biological synthesis of nanoparticles
Sanket Reply
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
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Source:  OpenStax, Basic physics for medical imaging. OpenStax CNX. Feb 17, 2014 Download for free at http://legacy.cnx.org/content/col11630/1.1
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