# 29.2 Discovery of the parts of the atom: electrons and nuclei  (Page 2/7)

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To see how the amount of deflection is used to calculate ${q}_{e}/{m}_{e}$ , note that the deflection is proportional to the electric force on the electron:

$F={q}_{e}E.$

But the vertical deflection is also related to the electron’s mass, since the electron’s acceleration is

$a=\frac{F}{{m}_{e}}\text{.}$

The value of $F$ is not known, since ${q}_{e}$ was not yet known. Substituting the expression for electric force into the expression for acceleration yields

$a=\frac{F}{{m}_{e}}=\frac{{q}_{e}E}{{m}_{e}}\text{.}$

Gathering terms, we have

$\frac{{q}_{e}}{{m}_{e}}=\frac{a}{E}\text{.}$

The deflection is analyzed to get $a$ , and $E$ is determined from the applied voltage and distance between the plates; thus, $\frac{{q}_{e}}{{m}_{e}}$ can be determined. With the velocity known, another measurement of $\frac{{q}_{e}}{{m}_{e}}$ can be obtained by bending the beam of electrons with the magnetic field. Since ${F}_{\text{mag}}={q}_{e}\text{vB}={m}_{e}a$ , we have ${q}_{e}/{m}_{e}=a/\text{vB}$ . Consistent results are obtained using magnetic deflection.

What is so important about ${q}_{e}/{m}_{e}$ , the ratio of the electron’s charge to its mass? The value obtained is

$\frac{{q}_{e}}{{m}_{e}}=-1\text{.}\text{76}×{\text{10}}^{\text{11}}\phantom{\rule{0.25em}{0ex}}\text{C/kg (electron).}$

This is a huge number, as Thomson realized, and it implies that the electron has a very small mass. It was known from electroplating that about ${\text{10}}^{8}\phantom{\rule{0.25em}{0ex}}\text{C/kg}$ is needed to plate a material, a factor of about 1000 less than the charge per kilogram of electrons. Thomson went on to do the same experiment for positively charged hydrogen ions (now known to be bare protons) and found a charge per kilogram about 1000 times smaller than that for the electron, implying that the proton is about 1000 times more massive than the electron. Today, we know more precisely that

$\frac{{q}_{p}}{{m}_{p}}=\text{9.58}×{\text{10}}^{7}\phantom{\rule{0.25em}{0ex}}\text{C/kg}\left(proton\right),$

where ${q}_{p}$ is the charge of the proton and ${m}_{p}$ is its mass. This ratio (to four significant figures) is 1836 times less charge per kilogram than for the electron. Since the charges of electrons and protons are equal in magnitude, this implies ${m}_{p}=\text{1836}{m}_{e}$ .

Thomson performed a variety of experiments using differing gases in discharge tubes and employing other methods, such as the photoelectric effect, for freeing electrons from atoms. He always found the same properties for the electron, proving it to be an independent particle. For his work, the important pieces of which he began to publish in 1897, Thomson was awarded the 1906 Nobel Prize in Physics. In retrospect, it is difficult to appreciate how astonishing it was to find that the atom has a substructure. Thomson himself said, “It was only when I was convinced that the experiment left no escape from it that I published my belief in the existence of bodies smaller than atoms.”

Thomson attempted to measure the charge of individual electrons, but his method could determine its charge only to the order of magnitude expected.

Since Faraday’s experiments with electroplating in the 1830s, it had been known that about 100,000 C per mole was needed to plate singly ionized ions. Dividing this by the number of ions per mole (that is, by Avogadro’s number), which was approximately known, the charge per ion was calculated to be about $1\text{.}6×{\text{10}}^{-\text{19}}\phantom{\rule{0.25em}{0ex}}\text{C}$ , close to the actual value.

#### Questions & Answers

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
anyone know any internet site where one can find nanotechnology papers?
Damian Reply
research.net
kanaga
sciencedirect big data base
Ernesto
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.
Bharti
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
Daniel
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Akash Reply
it is a goid question and i want to know the answer as well
Maciej
characteristics of micro business
Abigail
for teaching engĺish at school how nano technology help us
Anassong
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
NANO
what is fullerene does it is used to make bukky balls
Devang Reply
are you nano engineer ?
s.
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.
Tarell
what is the actual application of fullerenes nowadays?
Damian
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.
Tarell
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.
Virgil
is Bucky paper clear?
CYNTHIA
carbon nanotubes has various application in fuel cells membrane, current research on cancer drug,and in electronics MEMS and NEMS etc
NANO
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.
Harper
Do you know which machine is used to that process?
s.
how to fabricate graphene ink ?
SUYASH Reply
for screen printed electrodes ?
SUYASH
What is lattice structure?
s. Reply
of graphene you mean?
Ebrahim
or in general
Ebrahim
in general
s.
Graphene has a hexagonal structure
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what is biological synthesis of nanoparticles
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how did you get the value of 2000N.What calculations are needed to arrive at it
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Source:  OpenStax, College physics -- hlca 1104. OpenStax CNX. May 18, 2013 Download for free at http://legacy.cnx.org/content/col11525/1.1
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