+

Y = S + B

I3 = Q + ½Y

–

K+K0

K0K–

00

The NucleusAtoms consist of a positively charged nucleus plus electrons•Nuclear charge is Ze, where Z is an integer called the atomic number

•This determines what chemical element it is

2 2 2938.27203 MeV/ .51100 MeV/ .00001 MeV/Hm c c c Atom Nucleusm m

Nucleus Atom em m Zm

eZm bindingm

+Ze-e

-e-e

-e•The mass/potential energy (E0=mc2) of a neutral atom has three components:

•The mass of the nucleus•The mass of the electrons – there are Z of these•The binding energy of the electrons

•Binding energy is tiny, so

Tables of isotopes give the mass of the neutral atom in u

The Mass of an atom•Not all neutral atoms of the same element have the same mass

•Atoms come in different isotopes with different masses•All isotopes have masses that are approximately integer multiples of the same common unit•The atomic mass unit (u) is defined as 1/12 of 12C atom•The integer closest to M/u is called A, the mass number

11Li: 11.0438 u118Sn: 117.9016 u uM A 12 21

12u C 931.494 MeV/m c

Avogadro’s number•The ratio of u to g is called Avogadro’s number

•Useful for lots of problems

231 g6.022 10

1 uAN

The size of the nucleus•Can be measured in various ways

•My favorite: replace an electron by the 200 times heavier muon•Wave function is 200 times smaller•The wave function responds to the finite nuclear size

•Radius goes crudely as A1/3

•Volume roughly proportional tonumber of nucleons

1/30R R A

0 1.2 fmR

•Isotopes are described by telling their charge Z, their atomic mass number A, and the name of the chemical symbol

•The chemical symbol X tells you Z, so normally skipped•Sometimes an isotope has a bit of extra energy – we call it an isomer

•Denoted by putting a * on it•Almost always very unstable

or A AZ X X

Naming isotopes

*A X

+Ze

The composition of the nucleusAll normal nuclei have only two types of particles in them:•The proton has charge +e

•There are Z of these•The neutron has charge 0

•There are N of these•Electrons are not found in the nucleus

•The mass of an atom is protons + neutrons + electrons + binding•To a crude approximation, this is just the number of protons + neutrons•This is why the mass is almost an integer um Z N

+e +e0

0

# Particle Mass QZ Proton 1.007276 u +eN Neutron 1.008665 u 0 Electron 0.000549 u -e

A Z N

What is Z, N, A, and the approximate mass of 235U?

235A 235 uM 92Z

235 92 143N

Radioactivity•Many nuclei decay over time

•This is a quantum mechanical process – you can’t predict when it will happen•If you have a lot of atoms, the rate at which they decay will be proportional to the number of atoms•The radioactivity destroys the atoms R N dN

dt dN

dtN

ln N t k

•Integrate to see how number changeswith time

•N is number of atoms•N0 is initial number of atoms is the decay rate

•Also, multiply by •R is the rate at which atoms are decaying•R0 is the initial rate

0tN N e

0tR R e

•Half-life, t1/2 is the time it takes for half the atoms to decay•Let’s find a formula for it

1/210 02

tN N e 1/2 2te 1/2 ln 2t

Sample problem134Cs has a half-life of 2.065 y.•What is the decay rate ?•If we start with 1.000 g, what is the initial decay rate?•How long must we wait until the decay rate is less than 1.000 Ci = 3.700 104 s-1?

1/2

ln 2

t

0.692

2.065 y 10.3357 y

6

0

1.000 10 g

133.9067 u

MN

m

6 2310 6.022 10

133.9067

0 0R N 1 150.3357 y 4.496 10 15 1

7

1.509 10 y

3.166 10 s/y

7 14.784 10 s

0tR R e 0t R

eR

7 1

4 1

4.784 10 s1293

3.700 10 s

ln 1292 7.164t 1

7.164 7.164

0.3357 yt

21.34 yt

154.497 10

Particles and anti-particles•Several particles are important for understanding nuclear processes•Protons, neutrons, and electrons have already been discussed•The photon is a particle of light•The neutrino is a massless (or nearly massless) neutral particle

Particle Mass (MeV) Sym. Proton 1.007276 u p+ Neutron 1.008665 u n0

Electron 0.000549 u e-

Photon 0.000000 u Neutrino 0.000000 u anti-Elec. 0.000549 u e+

anti-Neut. 0.000000 u

p+

n0

e-

e+

Anti-Particles•For every particle, there is an anti-particle

•Same mass, opposite charge•Some particles (the photon) are their own anti-particles

•For nuclear physics, the important ones are the anti-electron and anti-neutrino

Neutron decay and anti-particlesParticle processes are a lot like equations•You can turn them around and they still work•You can move particles to the other side by “subtracting them”

•This means replacing them with anti-particles•(However, you have to make sure energy works)

p+n0 e-

•The neutron (in isolation) is an unstable particle•Decays to proton + electron + anti-neutrino

•This occurs in – decay + +

p+ e-+ + n0•Turn the reaction around•Put the neutrino on the other side•This occurs in electron capture p+ e-+ n0 +

•Put the electron on the other side•This occurs in + decay p+ n0 + + e+

Calculating Energetics in a decayNuclear decay is when an isolated nucleus spontaneously breaks apart•Typically (not always), there is one Parent nucleus and one Daughter nucleus•Also, typically, some other particles too

P D + ?We want to know how much energy is released•The potential energy of each component is just mc2

•The difference between these values is Q – the energy available•Unfortunately, we aren’t given the nuclear masses, just the atomic nuc 2 nuc 2 2

?P DQ M c M c m c Nuc Atom

eM M Zm

Atom 2 Atom 2 2?P P e D D eQ M Z m c M Z m c m c

2 2 2?P D D P eQ M M c Z Z m c m c

•This energy generally appears as kineticenergy, mostly of the lighter products on the right (the ? particles)

This formula is just a bridge to the formulas

we really want

Nuclear Decay Processes•There are many types of decay processes, we will focus on only the most common•Our goal is to figure out how to calculate, for those we consider:

•The daughter isotope (Z,A)•The energy Q produced•Whether the process actually occurs

•Processes can occur if Q > 0•We won’t worry about

•How slowly it goes (some virtually never occur) (higher Q helps)•Which are more likely than others (higher Q helps)

– decay•Electron capture+ decay•Spontaneous fission

decay decay

P D + ?

– decay – is another name for the electron and + for the positron•A neutron inside a nucleus can decay to a proton•Example: 3H 3He p+

n0

n0p+e-

•The daughter nucleus:•Total number of nucleons unchanged•Charge increases by 1•(Z,A) (Z+1,A)

•The change in energy (Q):

2 2 2 2P D D P e eQ M M c Z Z m c m c m c

2 2 21 0P D e eM M c m c m c

2P DQ M M c

p+n0 e-+ +

p+

p+ p+

n0 n0

n0

Electron capture

•A proton in the nucleus captures one of the electrons in the atom•Example: 7Be 7Li

•The daughter nucleus:•Total number of nucleons unchanged•Charge decreases by 1•(Z,A) (Z-1,A)

•The change in energy (Q):

2 2 2 2P D D P e eQ M M c Z Z m c m c m c

2 2 21 0P D e eM M c m c m c

2P DQ M M c

p+ e-+ n0 +

e-

p+n0

•A proton in the nucleus decays to a neutron•Example: 11C 11Be

•The daughter nucleus:•Total number of nucleons unchanged•Charge decreases by 1•(Z,A) (Z-1,A)

•The change in energy (Q):

2 2 2 2P D D P e eQ M M c Z Z m c m c m c

2 2 21 0P D e eM M c m c m c

2 22P D eQ M M c m c

+ decay

p+

p+p+

p+p+

n0

n0n0

n0

n0p+n0

p+ n0 + + e+

e+

Sample problemWhat would be the resulting isotope and theQ-value for each of the following decays of 40K?(a) - decay (b) electron capture (c) + decay

Z el. A mass (u)18 Ar 36 35.967547

37 36.96677638 37.96590339 38.96431440 39.96238442 41.963049

19 K 39 38.96370840 39.96400041 40.96182742 41.96240443 42.960716

20 Ca 40 39.96259141 40.96227942 41.95861843 42.85876744 43.95548146 45.95368748 47.952534

- decay: (Z,A) (Z+1,A)•Daughter is 40Ca

2P DQ M M c

2

2

u 931.494 MeV/

2 1.022 MeVe

c

m c

239.964000 39.962591 uc .001409 931.5 MeV 1.312 MeV

Sample problemWhat would be the resulting isotope and theQ-value for each of the following decays of 40K?(a) - decay (b) electron capture (c) + decay

Z el. A mass (u)18 Ar 36 35.967547

37 36.96677638 37.96590339 38.96431440 39.96238442 41.963049

19 K 39 38.96370840 39.96400041 40.96182742 41.96240443 42.960716

20 Ca 40 39.96259141 40.96227942 41.95861843 42.85876744 43.95548146 45.95368748 47.952534

239.964000 39.962384 uc

2

2

u 931.494 MeV/

2 1.022 MeVe

c

m c

.001616 931.5 MeV 1.505 MeV

Electron capture: (Z,A) (Z-1,A)•Daughter is 40Ar

2P DQ M M c

+ decay: (Z,A) (Z-1,A)•Daughter is 40Ar

2 22P D eQ M M c m c 1.505 1.022 MeV

0.483 MeV

•A large nucleus has a lot of electrostatic repulsion•It would like to separate, but strong forces hold it together

•More on this later•It is possible, but rare for it to break apart into two (or more) pieces•Commonly, neutrons are emitted as well.

Spontaneous Fission

•A quantum tunneling process•Very rare when large chunks are involved•No naturally occurring elements

•We need a small, very stable chunk to make this work better•The particle is such a chunk

P D1D2 n0n0

•The particle is the nucleus of Helium – it is very stable•Two protons and two neutrons

•Because it is light, it has a good chance of tunneling out

Decayp+ p+

n0

n0

PD p+ p+

n0

n0

•The daughter nucleus:•Nucleons decrease by four•Charge decreases by two•(Z,A) (Z–2,A–4 )

•The change in energy (Q):

2 2 2P D D P eQ M M c Z Z m c m c

2 2 22P D eM M c m c m c •m

+ 2me is just the mass of a helium atom

24P D HeQ M M M c

•Sometimes, nuclei have internal energy•Like an atom in an excited state

•Like an atom, the energy comes out in the form of a photon

Decay

P

•The daughter nucleus:•No change in nucleons•(Z,A)* (Z,A )

•The change in energy (Q):

2 2P DQ M M c m c

2P DQ M M c

D

How did we get an excited nucleus in the first place?•Usually a byproduct of a previous nuclear decay

60 60 **Co Ni e 60 ** 60 *Ni Ni 1.17 MeV

60 * 60Ni Ni 1.33 MeV

To us, this just looks like it came from the Cobalt

Summary

Radiation HazardsAll of these processes (except electron capture) produce high-energy ionizing radiation that can be extremely damaging to you particles are easily stopped, by paper or dead skin, if they are outside your body radiation can penetrate more deeply, so they are more dangerous radiation is very penetrating, and hence is most dangerous

Decay Z A Formula for Q +2 +4 (MP – MD – M4He)c2

– +1 0 (MP – MD)c2

e.c. –1 0 (MP – MD)c2

+ –1 0 (MP – MD)c2 – 2 mec2

0 0 (MP – MD)c2