Transcript Particle physics experiment - Univerzita Karlova v Praze

Scales of the microworld
Jiří Dolejší, Olga Kotrbová, Charles University Prague
We look at the world from our human point of view and the basic scale is
related to human dimensions:
• We are born about 0.5 meter big and we gradually grow to about 1.5 – 2
meters, interesting dimensions are e.g. 0.9-0.6-0.9 m etc.
• We start with a mass of few kilograms and we gradually reach tens or
maximum few hundreds kg
• The typical time intervals which we can perceive range from fractions
of seconds (sometimes deciding between life and death on the streets)
to tens of years of our life (i.e. from 10-1 s to about 102 y ≈ 109 s, since
1 year approximately equals p.107 s – check it for yourself)
• we are capable of carrying and lifting our weight with some load, i.e.
about 102 kg to the peaks with a speed of about 500 m per hour, what
means the power of mgDh/Dt = 102.10.500/3600 watt = 140 W. This is
just one fifth of the horse power (745 W) and twice the power which is
usually called the manpower (1/10 of HP). 5 hour climb with this rate
means the work of 2 500 000 joule = 2.5 MJ. We need about 10 MJ per
day in food even if we do “almost nothing”...
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What about atomic scales? Let us try to get there!
We can try to cut some macroscopic thing into microscopic pieces – I decided
to cut something eatable - a piece of chocolate. I proceeded by halving ...
100 g = 10-1 kg
100/15 g
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1/2 1/22 1/23 1/24
1/25 1/26 1/27 1/28 1/29
1/210 1/211 1/212 1/213 1/214
100/15 . 1/214 g =
= 4.10-4 g =
= 0.4 mg
How close to
atoms we are???
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It took centuries to learn atomic dimensions and properties. Today we know,
that a typical length scale for atoms is 10-10 m and their mass is of the order
10-27 – 10-25 kg. The lightest particle is the electron with mass 10-30 kg.
Mass scale
the smallest piece
of chocolate I can see
our body
103
1
10-3
10-6
10-9
10-12
atom
10-15
10-18
10-21
10-24
electron
10-27
10-30
kg
Length scale
the smallest piece
of chocolate I can see
the light
wavelength
our body
1
10-3
10-6
10-9
the atomic nucleus
electron
atom
10-12
10-15
10-18
m
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The lesson we may learn from the chocolate cutting is that atoms are far much
smaller and lighter than we can imagine. We can hardly get oriented in this
world by our common sense, we should rather rely on different estimates. One
important help are smart units. For mass we can use a quite natural unit close
to the mass of the lightest atom (H) ... “atomic mass unit” u, which is defined
as 1/12 of the mass of carbon (12C) atom.
1 u = 1.660 538 7 × 10-27 kg
Another useful mass unit is introduced with the help of the Einstein energymass relation E = mc2: We can express mass in terms of energy divided by c2.
The most frequently used units for measuring energy in the microworld are
electronvolts:
1 eV = 1.602 176 46 × 10-19 J,
1 eV/c2 = 1.782 661 73 × 10-36 kg
1 u = 931.494 01 MeV/c2
We do not expect that anybody will memorize these awkward numbers. But it
is helpful to remember the proton and electron mass, c and eV to J conversion:
mproton ≈ u ≈ 1 GeV/c2, melectron ≈ 0,5 MeV/c2
1 eV ≈ 1,6 × 10-19 J, c ≈ 3 × 108 m/s
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The mass and length scale again
the smallest piece
of chocolate I can see
our body
103
1
10-3
10-6
10-9
10-12
atom
10-15
10-18
10-21
10-24
TeV
electron
10-27
10-30 kg
GeV MeV /c2
It is rather easy to accommodate the length scale to the microworld – it is
sufficient to use the appropriate prefixes – fractions of nanometer for atoms
and femtometers for nuclei. Look to chapter 2 for the detailed description of
the experiment revealing the structure of an atom. You may also meet
angström (1 Å = 10-10 m) and fermi (1 F = 1 fm = 10-15 m).
1012
109
T
G
tera giga
106
103
M
k
mega kilo
1
10-3
m
mili
10-6
10-9
10-12
m
n
p
micro nano pico
10-15
f
femto
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As the atoms are so small, there is plenty of them in any piece of matter – the
Avogadro number (6.022 142 0 × 1O23) in each mol. Let us calculate how many
atoms are in a glass of water (say 0.2 liter).
Volume × density =
= mass of the water
mass divided by molar mass
(2×1+16=18 g for H2O)
V .
200cm3 .1 g/cm3
number of H atoms
N Avogadro .2 
6.0 1023 mol1.2 
mmol H 2O
18 g/mol
 1.3 1025
Two H atoms
per H2O molecule
What is the average volume occupied by one water molecule? The are 0,67
× 1025 water molecules in the mentioned glass, so
200 cm3
 23
3
 29
3
3
VH 2O molecule 

3
.
0

10
cm

3
.
0

10
m

0
.
03
nm
0.67 1025
If the volume has a form of a cube, its edge will have a length 0.3 nm.
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Expert pages! You don´t need to understand them, but it is a challenge!
Could you calculate the energy of a proton falling from the infinity to the Earth surface
(neglecting air)? Comment: We have in mind that the gravity is an effective accelerator, at least
for stones, planes, suicides etc. and so we expect quite significant energy...
Maybe you remember that potential of the field is the helpful quantity to solve our question, you
met the potential of the central gravitational field and/or of the central Coulombic field. This
potential is equal zero at infinity and at given distance r from the source it has a value
 gravitation  
M
1 Q
,  electric 
r
4p 0 r
The minus sign in the gravitational potential says that a body with mass m has the negative
potential energy E = f(r) m. The body is bounded by the gravitation, we should supply the energy –
E to free it. We can call |E| = -E the binding energy of this body in the field. In our case we
consider proton at rest at infinity (zero kinetic, potential and total energy), which will be
accelerated by the attractive force (it gains positive kinetic energy which compensates negative
potential energy keeping the total energy zero). The kinetic energy of the proton we can use for
experiments, this is the quantity we are interested in:
Ep kin  mp gravitation ( REarth )  mp
M Earth
M
 mp  2Earth REarth  mp gREarth
REarth
REarth
Ep kin  1.6 1027 kg 9.8 ms2 6400km  1.110-19 J  0.7 eV
This is the acceleration
of gravity g
So the electrical field created from the AA cell from your walkman accelerates proton more
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than the Earth's gravitational field!!!
The energy scale
As we already said the most frequently used unit in the microworld is the
electronvolt.
Rest
energy
of a
mosquito
My kinetic
energy
when
walking
Kinetic
energy
of a flying
mosquito
Rest
energy
of an
atom
Rest
energy
of an
electron
Photons
energies
in visible
light
Thermal
energy
of an
atom
1joule
1030
1027
1024
Human daily
power
consumption
1021
1018
1015
Highest energy of
a single particle
observed in
cosmic radiation
Energy contained
in a glass of beer
(0.5 liter)
1012
109
106
103
(TeV) (GeV) (MeV) (keV)
Binding energies
of nucleons in
nuclei
Highest proton
energy from
current accelerator
(Tevatron in FNAL)
1
(eV)
10-3 eV
(meV)
Binding energies
of electrons in
atoms
Energy
of an
electron
in the TV
Proton
energy
from “free
fall example”
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To be continued
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