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Electrical potential energy converted to kinetic energy

Calculate the final speed of a free electron accelerated from rest through a potential difference of 100 V. (Assume that this numerical value is accurate to three significant figures.)

Strategy

We have a system with only conservative forces. Assuming the electron is accelerated in a vacuum, and neglecting the gravitational force (we will check on this assumption later), all of the electrical potential energy is converted into kinetic energy. We can identify the initial and final forms of energy to be KE i = 0, KE f = ½ mv 2 , PE i = qV , and PE f = 0.

Solution

Conservation of energy states that

KE i + PE i = KE f + PE f .

Entering the forms identified above, we obtain

qV = mv 2 2 . size 12{ ital "qV"= { size 8{1} } wideslash { size 8{2} } ital "mv" rSup { size 8{2} } "." } {}

We solve this for v size 12{v} {} :

v = 2 qV m . size 12{v= sqrt { { {2 ital "qV"} over {m} } } "." } {}

Entering values for q , V , and m size 12{q, V", and "m} {} gives

v = 2 –1.60 × 10 –19 C –100 J/C 9.11 × 10 –31 kg = 5.93 × 10 6 m/s.

Discussion

Note that both the charge and the initial voltage are negative, as in [link] . From the discussions in Electric Charge and Electric Field , we know that electrostatic forces on small particles are generally very large compared with the gravitational force. The large final speed confirms that the gravitational force is indeed negligible here. The large speed also indicates how easy it is to accelerate electrons with small voltages because of their very small mass. Voltages much higher than the 100 V in this problem are typically used in electron guns. Those higher voltages produce electron speeds so great that relativistic effects must be taken into account. That is why a low voltage is considered (accurately) in this example.

Section summary

  • Electric potential is potential energy per unit charge.
  • The potential difference between points A and B, V B V A size 12{V rSub { size 8{B} } -V rSub { size 8{A} } } {} , defined to be the change in potential energy of a charge q size 12{q} {} moved from A to B, is equal to the change in potential energy divided by the charge, Potential difference is commonly called voltage, represented by the symbol Δ V size 12{V= { {"PE"} over {q} } "." } {} .
    Δ V = ΔPE q and ΔPE = q Δ V . size 12{?V= { {?"PE"} over {q} } " and "D"PE="q?V "." } {}
  • An electron volt is the energy given to a fundamental charge accelerated through a potential difference of 1 V. In equation form,
    1 eV = 1.60 × 10 –19 C 1 V = 1.60 × 10 –19 C 1 J/C = 1.60 × 10 –19 J.
  • Mechanical energy is the sum of the kinetic energy and potential energy of a system, that is, KE + PE . size 12{"KE"+"PE"} {} This sum is a constant.

Conceptual questions

Voltage is the common word for potential difference. Which term is more descriptive, voltage or potential difference?

If the voltage between two points is zero, can a test charge be moved between them with zero net work being done? Can this necessarily be done without exerting a force? Explain.

What is the relationship between voltage and energy? More precisely, what is the relationship between potential difference and electric potential energy?

Voltages are always measured between two points. Why?

How are units of volts and electron volts related? How do they differ?

Problems&Exercises

Find the ratio of speeds of an electron and a negative hydrogen ion (one having an extra electron) accelerated through the same voltage, assuming non-relativistic final speeds. Take the mass of the hydrogen ion to be 1 . 67 × 10 27 kg . size 12{1 "." "67"×"10" rSup { size 8{-"27"} } " kg" "." } {}

42.8

Questions & Answers

where we get a research paper on Nano chemistry....?
Maira Reply
what are the products of Nano chemistry?
Maira Reply
There are lots of products of nano chemistry... Like nano coatings.....carbon fiber.. And lots of others..
learn
Even nanotechnology is pretty much all about chemistry... Its the chemistry on quantum or atomic level
learn
Google
da
no nanotechnology is also a part of physics and maths it requires angle formulas and some pressure regarding concepts
Bhagvanji
Preparation and Applications of Nanomaterial for Drug Delivery
Hafiz Reply
revolt
da
Application of nanotechnology in medicine
what is variations in raman spectra for nanomaterials
Jyoti Reply
I only see partial conversation and what's the question here!
Crow Reply
what about nanotechnology for water purification
RAW Reply
please someone correct me if I'm wrong but I think one can use nanoparticles, specially silver nanoparticles for water treatment.
Damian
yes that's correct
Professor
I think
Professor
Nasa has use it in the 60's, copper as water purification in the moon travel.
Alexandre
nanocopper obvius
Alexandre
what is the stm
Brian Reply
is there industrial application of fullrenes. What is the method to prepare fullrene on large scale.?
Rafiq
industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
Damian
How we are making nano material?
LITNING Reply
what is a peer
LITNING Reply
What is meant by 'nano scale'?
LITNING Reply
What is STMs full form?
LITNING
scanning tunneling microscope
Sahil
how nano science is used for hydrophobicity
Santosh
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
Rafiq
what is differents between GO and RGO?
Mahi
what is simplest way to understand the applications of nano robots used to detect the cancer affected cell of human body.? How this robot is carried to required site of body cell.? what will be the carrier material and how can be detected that correct delivery of drug is done Rafiq
Rafiq
if virus is killing to make ARTIFICIAL DNA OF GRAPHENE FOR KILLED THE VIRUS .THIS IS OUR ASSUMPTION
Anam
analytical skills graphene is prepared to kill any type viruses .
Anam
Any one who tell me about Preparation and application of Nanomaterial for drug Delivery
Hafiz
what is Nano technology ?
Bob Reply
write examples of Nano molecule?
Bob
The nanotechnology is as new science, to scale nanometric
brayan
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Damian
Is there any normative that regulates the use of silver nanoparticles?
Damian Reply
what king of growth are you checking .?
Renato
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
?
Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
Adin
why?
Adin
what school?
Kyle
biomolecules are e building blocks of every organics and inorganic materials.
Joe
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
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Source:  OpenStax, College physics (engineering physics 2, tuas). OpenStax CNX. May 08, 2014 Download for free at http://legacy.cnx.org/content/col11649/1.2
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