Nuclear Physics Flashcards
Which experiment disproved the plum pudding model?
The Rutherford Scattering experiment
What was Rutherford’s scattering experiment?
A stream of alpha particles are fired from a radioactive source at very thin gold foil. When the alphas strike a fluorescent screen, there is tiny visible flash of light on screen/ The scientists recorded the numbers of flashes on screen and their angles.
What did the scientists first expect when doing Rutherford’s scattering experiment, and what were their results?
If the Plum pudding model was right, all flashes should have been seen within a small angle of the beam. They saw most particles went straight through the foil, a few scattered at angles greater than 90, deflected back the way they came.
What were the results of the Rutherford scattering experiment?
Most alpha particles went straight through the foil. Some were deflected at large angles. Very few were deflected at angle greater than 90, coming back the way they came.
Conclusion learnt from most of the alpha particles going through the gold foil in Rutherford Scattering experiment?
Atom is mostly empty space
Conclusion learnt from some alphas being deflected at large angles in Rutherford experiment?
Center must have large, positive charge, the nucleus, to repel the particles
Conclusion learnt from the very few alphas being deflected so much (greater than 90) that they came back the way they came
Nucleus is more massive than alpha particles, as the alphas could only be scattered by something more massive than themselves.
Conclusion learnt from very few alphas deflected at angle greater than 90, coming back from where they came, while most went through
Diameter of nucleus must be tiny when compared to the diameter of the atom
What was the conclusion about the structure of the atom after Rutherford’s experiment
Most mass and positive charge in atom must be contained in tiny, central nucleus.
What is the structure of an atom
There is a positive nucleus containing nucleons of protons, which are positive charge, and neutrons, neutral charge. Electrons orbit the nucleus
What is the charge of an electron
-1.6 x 10^-19 C. Equal and opposite to the charge of a proton, +1.6 x 10^-19 C.
What is the position of protons, neutrons and electrons in atom
Electrons orbit nucleus at VAST distances, so atoms are mostly empty space. Proton and Neutrons are much more massive than electrons, so nucleus makes up almost all of the mass of the atom
What is proton number and its symbol
Number of protons in an atom. Symbol: Z.
What is the relationship between protons and electrons in a neutrally charged element
Number of protons = number of electrons
What is a proton number used to identify
Defines element. No 2 elements have the same proton number.
What is nucleon number or atomic mass, it’s symbol and qualities
Number of nucleons in atom (protons and neutrons). Symbol: A
How is nucleon number the same as atomic mass
Protons and neutrons have an atomic mass of 1, and electron mass is negligible as it is very small, so nucleon number is same as atomic mass
What is nucleon number used for
To know number of neutrons and protons in atom, as well as the mass of the atom
What is electric current caused by
The flow of negatively charged electrons
What is the relationship between electric current and magnetic fields
The charged particles in a current are affected by magnetic field, so a current carrying wire can experience a force in a magnetic field.
What do you use F=BQv to find
The force acting on a single charged particle moving through a magnetic field
How do charge particles in a magnetic field move in particle accelerators
They are deflected in a circular path using the principle that magnetic field is always perpendicular to direction of motion.
How does a particle follow a circular path in a cyclotron
Charged particles are fired into one of the electrodes. The magnetic field makes them follow a semicircular path and then leave the electrode.
How does the particle jump between electrodes in a cyclotron
Potential difference is applied between electrodes, which accelerates the particles across the gap until they enter the next electrode.
Why does the particle have a larger turning radius each time it circles in the cyclotron
Since the particle was accelerated within the gap, it now has a higher speed, which means momentum is higher. p=mv and v is higher. So the particle follows a circular path with a larger radius than last time before leaving the electrode.
How is the charged particle attracted to each electrode despite each D having opposite charges
The p.d is on the electrodes is reversed, so as, i.e, the negative particle has just left the positive charged D and is in the gap, the negative D now alternates in current, becoming positively charged, while the first D becomes negative. So particle is pulled in by the positive D and repelled by the negative D, accelerating it.
How does the particle exit the cyclotron
The positive, negative alternation of electrodes repeats as particle spirals outwards due to increasing momentum and so increasing radius, before eventually exiting the cyclotron
In a cyclotron, what happens once the particle reaches relativistic speeds
At that point, the turning radius has reached its maximum and cannot increase more, as speed has reached it’s maximum. But mass is now increasing, so in order to keep the same turning radius, magnetic field strength must keep increasing to maintain the radius, otherwise, momentum decreases since p=mv……idk ask chris tomorrow
What is a cyclotron
A type of particle accelerator, made of two D shaped electrodes (insert image)
What is an electron volt
The kinetic energy carried by an electron after it has been accelerated through a p.d of 1 volt.
What is the equation for electron volt
eV = 1/2mv^2
What is the energy in eV of an electron accelerated by a p.d
energy gained by electron (eV) = accelerating p.d. (V)
How much joules is 1eV
1.60 x 10^-19 J
What is a linear accelerator
A linac is a long, straight tube containing a series of tube shaped electrodes. The charge on each electrode alternates along the tube, so positive, negative, positive… (INSERT IMAGE)
In a linac, how does the charged particle accelerate between electrodes if they are oppositely charged
The electrodes are connected to an alternating p.d supply so the charge of each continuously changes between + and -. This means electric field between each pair of electrodes is continuously changing direction. So the particle is always going to be attracted to the next electrode, and repelled by the previous.
How do the electrodes switch charge at the exact time the particle exits the previous electrode in a linac
The alternation is timed so particles are always attracted to the next electrode, and repelled from the previous one.
Linac, If the particle is accelerating each time it is in a gap between electrodes, so speed is increasing, how does the charge switch exactly when it needs to, if it is in a timed switch sequence?
To compensate for increasing speed, the length of the electrodes increases as the particle travels down the accelerator, so that the particle spends the same amount of time in each electrode. So the charge switch will happen every 5 seconds for example, but the tubes get longer so the particle always spends 5 seconds within each tube despite having higher velocity each time.
In a linac, do the tubes continue increasing in length once the particle reaches relativistic speeds, close to the speed of light
At that point, the tubes stay at the same size, because the speed increase is so very tiny, it is negligible. The tubes keep increasing in length until we hit relativistic speeds, at which point the tubes are the same size. There is a maximum length.
What do particles do once they leave the linac?
High energy particles leaving a linac collide with a fixed target at the end of the tube.
What is thermionic emission
When you heat a metal, its free electrons gain a lot of thermal energy. If you give them enough energy, they break free from the surface of the metal. This is thermionic emission.
How does an electron gun work
A heating coil heats the metal cathode. Electrons are accelerated towards the cylindrical anode by the electric field set up by high p.d. Some electrons pass through a little hole in the anode, making a narrow electron beam. Electrons in the beam move at a constant velocity, because there’s no field beyond the anode -i.e no force.
INSERT ELECTRON GUN IMAGE HERE
What is an electron gun used for
Accelerating electrons with an electric field. Often, the beam of electrons produced by the gun are directed with an applied magnetic field towards something. An example is an electron microscope, where electrons can be focused onto a sample using a magnetic field.
What is a proton number used to identify
Defines element. No 2 elements have the same proton number.
What is the relationship between protons and electrons in a neutrally charged element
Number of protons = number of electrons
What is a hadron
Any particle which is made up of quarks
What are examples of a hadron
Protons, Neutrons, Mesons
What are quarks
Fundamental particles. There is nothing a quark is made of. A quark is the most fundamental building block
What are the types of hadrons
Baryons and Mesons
What is a baryon
Protons and Neutrons are both baryons. Think of them like the same particle but with different charge. Sigmas are also baryons.
What is baryon decay
All baryons except protons decay to a proton. All of them are unstable, which means they decay to become other particles. The end result of a decaying particle depends on what it started as, but it always includes a proton. Protons are the only stable baryon, they don’t decay
What are antibaryons
Antiparticles of protons and neutrons, antiprotons and antineutrons.
What do anti-baryons do
Antiparticles are annihilated when they meet the corresponding particle. This means you don’t find anti-baryons in ordinary matter, as they have all been annihilated.
What is a baryon number
The number of baryons. It is similar to how protons have a +1 charge and electrons have a -1 charge. This value can only be a whole number. Protons, neutrons and sigmas have a baryon number of 1. Antiprotons, antineutrons have a baryon number of -1. Non-baryon particles like electrons have a baryon number of 0.
How can you use baryon number to check if a reaction is feasible
Baryon number must always be conserved in any interaction. So baryon number before an interaction must be the same as after an interaction. You can use this to predict whether an interaction will happen. If the numbers don’t match, it can’t happen. Total baryon number in any particle interaction never changes. (Before and after must be equal)
What are mesons
They are hadrons which are unstable, and have baryon number=0, so they are not baryons
What are pions
Pions (pi-mesons) are a type of meson. They are the lightest mesons.
What are the type of pions you get
You get π+, π0, π-, these have different electric charges.
Where do pions occur
You get lots of pions in high-energy particle collisions like those studied in CERN. Both pions and kaons were discovered in cosmic rays, cosmic ray showers are a source of both particles.
How long is a meson lifespan
Short, they are unstable so they only exist briefly before decaying
What are kaons
Another type of meson that is heavier and more unstable than pions
What are leptons
Leptons are NOT Hadrons because they are NOT made of quarks. They are fundamental particles as well
What are examples of leptons
Electrons, Muons, Tauons
What are muons and tauons
They are leptons and are like heavy electrons. Muons (μ-) are heavier than electrons but lighter than tauons, and Tauons (τ-) are the heaviest.
What charge do leptons have
All leptons have negative charge.
What do neutrinos do
Neutrinos (𝜈) have zero or almost zero mass and zero electric charge. They don’t do much. In fact, a neutrino an pass right through Earth without anything happening to it. Neutrinos exist to act as a balance for leptons.
What helps balance leptons
Neutrinos. Each lepton has its own neutrino. Electron (e-),
electron neutrino (𝜈_e),
Muon neutrino (𝜈_μ),
Tauon neutrino (𝜈_τ)
How do lepton numbers work
Unlike baryon number, where a protons, neutrons and sigmas all have baryon number of 1, there are different lepton numbers for each lepton.
L_e - Lepton number for electron
L_μ - Lepton number for Muon
L_τ - Lepton number for Tauon
A muon has a L_μ = 1, but an L_e = 0, L_τ = 0. Remember all leptons have charge of -1
What charge and lepton number do neutrinos have
All lepton neutrinos have charge = 0. They have a lepton number = 1 for their respective lepton. So a 𝜈_μ has a L_μ = 1, like a normal muon does, but has L_τ = 0 and L_e = 0.
What are the properties of photons in particle physics
No mass, no charge, no baryon number, no lepton number. But a photon has Energy.
What is a photon denoted as when it is involved in an interaction
γ. The gamma symbol
What are the properties
of a positron
Positrons are antileptons, so L_e = -1. They have identical mass to electrons but carry a positive charge.
What are antiparticles
Every particle has a corresponding antiparticle with the same mass as the particle, but opposite charge, and negative Lepton number, or baryon number. Even every lepton neutrino has a corresponding anti neutrino.
(INSERT CGP table here)
What formula converts mass into energy and vice versa
E = mc²
What must be conserved before and after a reaction
Mass energy. In chemistry, the mass of reactants must equal to the mass of products. In particle physics, mass before may not equal mass after, because some of the mass may be converted into energy. So the combination of mass energy is what must be conserved before and after.
What happens when energy is converted into mass in particle physics
When energy converts to mass, you have to make equal amounts of matter and antimatter
What may happen when you fire two protons at each other at high speeds
You will end up with a lot of energy at the point of impact This energy can form more particles. If an extra proton is created, there has to be an antiproton made to go with it. This is called pair production
What is pair production
When a particle is created, the antiparticle of the created particle is also created. When a proton is created, an antiproton is also created. They come in pairs.
What is needed to create particles that have a large mass
Large amounts of energy, due to mass energy conservation. If you want a particle with a large mass, you need to input a lot of energy to be converted into mass
What units are used for describing nuclear reactions for mass and energy
For energy, the electron volt, eV, is used instead of Joules. For mass, atomic mass units, u, or eV/c² are used instead of kg. Mega and Giga are often used with eV since an eV is so small.
How to convert from eV to joules
1eV = 1.6 x 10^-19
How to work out 1 atomic mass unit
1eV/c² = 1.60x10^-19J/3.00 x 10^8ms^-1)² = 1.78 x 10^-36 kg (to 3 s.f)
How is a particle-antiparticle pair produced
Each pair is produced from a single photon. If one photon has enough energy to produce that much mass
Where does pair production usually happen and why
It tends to happen near a nucleus, which helps conserve momentum
Which particle-antiparticle pair is usually produced in pair production and why
Electron-positron pairs produced rather than nay other, because they have a relatively low mass, so require less energy to produce.
What is the minimum energy a photon must have to do pair production
Minimum energy of photon must be the combined energy of the two particles (particle and antiparticle) due to their masses. This is assuming that the particles have negligible Kinetic energy.
How do you calculate minimum energy (E_ γ)
Using E=mc², both the particle and its antiparticle pair have the same mass, which means E_ γ = 2mc²
How do you calculate maximum wavelength or minimum frequency of photon
Using equation E_ γ= hc/λ = hf. Max wavelength because wavelength is the divisor in the bottom of the fraction, minimum frequency because frequency is in the numerator.
What happens when a particle meets or collides with an antiparticle
Annihilation. All the mass of the particle and antiparticle gets converted to energy, in the form of a pair of photons.
INSERT IMAGE ON PAGE 123
Why are the particle and antiparticle tracks curved in the image
INSERT IMAGE ON PAGE 123
Because there’s usually a magnetic field present in particle physics experiments. They curve in opposite directions because of the opposite charges on the electron and positron.
How do you calculate the minimum energy of each photon produced from annihilation (assuming KE is negligible)
The minimum combined energy of the photons will be equal to the combined energy of the particles due to their masses, so 2E_γ=2mc². The 2’s cancel out so E_γ=mc²
How long do antiparticles exist
Only a fraction of a second before they are annihilated, so you won’t see many of them.
What are quarks used for
To make hadrons (baryons and mesons)
Which quarks are needed to make protons and neutrons
Only up (u) and down (d) quarks
What does the strange (s) quark let you do
It allows you to make more particles with a property called strangeness
What are antiparticles of hadrons made of
Antiquarks
What is the charge of the up (u), down (d) and strange (s) quarks
Up quark is the only one with a +2/3 charge, the other 2 are -1/3
Up: +2/3
Down: -1/3
Strange: -1/3
Based on quarks, why do hadrons always have an whole number charge
Hadrons, at least baryons, all have 3 quarks, and since each quark has a charge that is some number of a /3, they will always add up to a whole number no matter the combination
What baryon number do up (u), down (d) and strange (s) quarks have
They all have baryon number of +1/3 as each baryon is made up of 3 of them
What is the strangeness value of up (u), down (d) and strange (s) quarks
Up and Down quarks have a strangeness value of 0. Strange quarks have a strangeness of -1.
What are the properties of antiquarks, anti-up quark (ū), anti-down quark (đ), and anti strange quark (S̄)
Whatever property their regular counterpart has, they have the opposite.
Anti-up quark has a charge of -2/3, baryon number of -1/3 and strangeness of 0 (because negative of 0 is still 0)
Anti-down quark Charge: +1/3, Baryon Number: -1/3 Strangeness: 0
Anti-strange quark Charge: +1/3, Baryon Number: -1/3 Strangeness: +1
INSERT TABLE ON 124
What are the three other quarks discovered, besides from up, down and strange
Top, bottom and charm
How was the top quark discovered
The bottom and charm quarks were discovered in 1970s, but most the quarks and leptons that were discovered so far came in pairs (up, down or electron, electron neutrino). It was predicted with symmetry of the model that there was a 6th quark, the bottom quarks pair. This was later detected in 1995.
Why do you not see top (t), bottom (b) and charm (c) quarks very often
They are quite unstable
What are the charges of top, bottom and charm quarks, the baryon number and strangeness.
top: +2/3
bottom: -1/3
charm: +2/3
They all have a baryon number of +1/3, and a strangeness of 0.
How do you find the quark composition of protons and neutrons
You know that they are only made of up and down quarks, and you know the charge of a proton and of a neutron. So you can use the charge of the quarks to work them out, find which combination gives you a +1 charge for proton, and 0 charge for neutron
What quarks is a proton made up of
up, up, down, uud
What quarks is a neutron made up of
up, down, down, udd
What quarks are anti-protons and anti neutrons made of
Whatever normal protons and neutrons are made of but anti versions.
anti-proton: anti-up, anti-up, anti-down
anti-neutron: anti-up, anti-down, anti-down
How did evidence for quarks come about
Hitting protons with high-energy electrons.
Why did hitting proton’s with high energy electrons provide evidence for quarks
High-energy electrons have a short de Broglie wavelength, which means they can be used to probe tiny distances in side a proton. The way the electrons got scattered after colliding showed that there are 3 concentrations of charge (quarks) inside a proton.
What are mesons made up of
They are made up of a quark, and an anti quark
What are pions made up of
Combinations of up, anti-up, down, and anti-down quarks
What is the relationship between π+ and π-, k+ and k-
π+ is the particle, π- is the anti-particle pair for it. k+ is the particle, k- is the anti-particle pari for it
What is the antiparticle pair of π^0
π^0 antiparticle pair is itself.
What are the 7 mesons
π+, π-, π^0, k+, k-, k^0, and k^-0. k^-0 exists because k^0 has a strangeness value, so to balance this value out, k^-0 has to exist with an opposite strangeness value. π^0 does not have a strangeness value
How do you deduce the quarks that mesons are made of
You know that pions are only made of up, down and their antipair quarks, you know that kaons have a combination of strange quark, or up/down quarks, and their antipair. You also know each mesons charge. So you can do combinations of up down, strange and their antipairs of quarks to deduce what they are made of.
INSERT HEXAGON FROM 125 HERE
Why can’t you get a quark by itself
If you try blasting a proton with enough energy, the energy just gets changed into more quarks ant antiquarks. So let’s say a proton (uud) gets blasted and one of the up quarks exits. There is pair production and an anti-up also gets produced, making a meson of π^0. It is not possible to get a quark by itself, this is called quark confinement.
PICTURE FROM 125
How do you represent particle interactions
With equations you can write either in terms of hadrons involved, or specific quarks (if one quark is changing into another). In beta minus decay, neutron decays into a proton (by a down quark turning into an up quark) and emits an electron, electron antineutrino pair.
in terms of hadrons n–> p + e- + ν ¯ e or in terms of quarks d–> u + e- + ν ¯ e
What three properties must always be conserved in any particle interaction for it to be feasible
Conservation of momentum and energy.
Charge must always be conserved. Total charge before must equal total charge after
Baryon number must always be conserved. Total baryon number before must equal total baryon number after.
And lepton number must be the same before and after an interaction has occured
Why should you be more careful when checking lepton number before and after an interaction
Each lepton is specific. So L_e must be the same before and after, L_μ must be the same before and after and L_τ must be the same before and after.
ν_μ + μ- –> e- + v_e is not feasible because L_μ=2, L_e = 0 before and L_μ=0, L_e=2 after. Lepton numbers are not conserved, so interaction is not possible
Is the interaction p–> n + e- + v_e possible
Charge is +1 before and -1 after, therefore reaction is not possible. If charge was fine, you would check baryon number, then finally lepton number to see if it was possible
How do you check if an interaction is possible
List out all of the properties of each particle underneath. Start by doing charge, then baryon number, then lepton number. If you see that charge is not conserved, you can stop and say interaction is not possible, you don’t have to continue with baryon number and lepton number.
What are the properties of an electron neutrino, and an electron antineutrino
v_e: electron neutrino has charge = 0, baryon number = 0 and L_e = +1.
v_e- : Anti-electron neutrino has a charge = 0, baryon number = 0 and an L_e = -1.
Remember. Neutrinos exist to BALANCE. They have no effect on the interaction, so no charge. Only number they have is whether they have an L_e or not
What do charged particles do when they pass through a substance
They cause ionisation, meaning electrons are knocked out of atoms. The particle leaves a trail of ions as it goes. (INSERT PICTURE on page 127). If we make this trail of ions show up and then take a photo, we can detect the particle
How does a cloud chamber work
Using super cooled vapor, something that’s still a gas below its usual condensation temperature. The ions left by particles make the vapour condense and you get vapour trails.
What do alpha-particles and beta-particles look like in cloud chambers
Heavy, short tracks mean lots of ionisation, which could be caused by alpha-particles. Fainter, long tracks come from particles that cause less ionisation, like beta-particles. The wider and shorter the track, the more ionisation the particle has caused.
INSERT CLOUD CHAMBER PHOTO FROM 127
How do bubble chambers work
They are like cloud chambers but in reverse. Hydrogen is kept as a liquid above its normal boiling point by putting it under pressure. If the pressure is suddenly reduced, bubbles of gas will form in the places where there is a trail of ions. You have to take a photo quickly before the bubbles grow too big.
Which particles do cloud chambers and bubble chambers only show
Both chambers only show charged particles, as these are the only ones that can leave a trail of ions.
How do charged particles moving in a magnetic field act
They will experience a force, making the particle follow a curved track
What is the equation you have to know relating to find the radius of a charged particles curved track
r = p/BQ
r - radius of charged particles curved track
p - momentum
B - magnetic flux density
Q - Charge on particle
What does a large curve radius of a particles curved track tell you
The larger the curve radius, the greater the particles momentum
How do positive and negative particles behave in a magnetic field.
They curve in opposite directions
How do you find out which particle is positive and which is negative from the spirals in a magnetic field
Using Flemings left hand rule. The direction of travel will tell you the charge
What patterns do you see a charged particle make in a magnetic field and why
You see spirals, as interactions with the detector decrease the kinetic energy, and so the momentum of the particle, so the spirals get smaller and smaller in size.
INSERT PICTURE IN 127
What other use does r = p/BQ have other than finding the radius
You can use it to work out the magnetic field you need to keep a charge in a particular radius of circular path. You do this by solving for B.
How can you tell if a neutral particle is present in a particle detector
Neutral particles don’t make tracks since they do not have charge. So when they are present, there will be a blank space followed by a V-shape. The v-shape is two oppositely charged particles coming from from the decay of a neutral particle. For example K^0 –> π+ + π-
INSERT PICTURE FROM 128
Why do some neutral particles travel further than others in a particle detector before decaying
The distance from the interaction point to the V depends on the half-life of the neutral particle. The longer the half-life, the further they travel before decaying.
Why do particles seem to survive for so long in a particle detector
The particles are traveling close to the speed of light, so they experience relativistic time dilation. That means that time seems to run more slowly for the moving particle than it does for you as a stationary observer, so they seem to survive for much longer than normal
Why do some particle tracks appear straight in a particle detector, despite there being a magnetic field
The particles have so much momentum that the tracks are almost straight
How do you identify positively and negatively charged particles in a bubble chamber photo
Find which way the little spirals curve. These are knock-on electrons so now you know which way negatively charged particles curve. Positively charged particles curve the opposite way. You can identify the charge of a particle from the way it curves. (INSERT PHOTO OF BUBBLE CHAMBER)
How do you identify where a reaction has happened from a photo of a bubble chamber
Find a point with several curved tracks coming from it. That’s a reaction
How do you find a knock on electron in a bubble chamber photo
Look for a LITTLE spiral coming from one of the straight tracks. (INSERT PHOTO BUBBLE CHAMBER)
What is a knock on electron in a bubble chamber photo and what do they tell you
An electron that has been kicked out of one of the hydrogen atoms.
(INSERT BUBBLE CHAMBER PHOTO SHOWING KNOCK ON ELECTRONS)
What do knock-on electrons tell you
Knock-on electrons tell you two things, which way the particles are going, and which way negative particles curve.
What should you do with the straight lines from a bubble chamber photo and why
Ignore the straight lines. They are from the incoming beam. They are just several particles that go straight through without doing anything. (INSERT PHOTO OF BUBBLE CHAMBER)
Are bubble chambers and cloud chambers still used today?
No, nowadays particle physicists use detectors that give out electrical symbols which get sent straight to a computer. It is easier than having a whole team of scientists squinting over thousands of photos.
How do you find a knock on electron
Look for a LITTLE spiral coming from one of the straight tracks. This is a knock-on electron, an electron that has been kicked out of one of the hydrogen atoms. Knock-on electrons tell you two things, which way the particles are going, and which way negative particles curve.
How do you identify positively and negatively charged particles in a bubble chamber photo
Find which way the little spirals curve. These are knock-on electrons so now you know which way negatively charged particles curve. Positively charged particles curve the opposite way. You can identify the charge of a particle from the way it curves.
In neutron decay
n -> p + e- + v_e-
Why is an electron anti neutrino produced
To balance the lepton number. Normal electron neutrinos have a lepton number of +1 and electrons also have a lepton number of +1. Since lepton number before the interaction is 0, the lepton number afterwards must also be 0. So an electron antineutrino is produced as it has a -1 lepton number