Nuclear Physics

Micro-world Macro-world

Lecture 16

Neutron

By 1930, the charge and masses of many differentnuclei were known. The charges were found to be Qnucleus = Z x proton charge & the masses wereMnucleus = A x proton mass

Z is always an integer A is nearly an integer

But, except for hydrogen where A=Z=1,A & Z are different.

Electrons in the nucleus?

One idea was that the nucleus contained A protonsand A-Z electrons.

But Heisenberg’s uncertainty principle forbids this:

Suppose x= 1x10-14m typical size of a nucleus

px > 6.6x10-34Js1x10-14m

= 6.6x10-28kgm/s

vx > px me

6.6x10-28Js9x10-31kg

= >speed of light

non-relativistic calculationis invalid

Correct calculation gives Eelectron > 2x106 eV,such electrons would not stay inside a nucleus

Discovery of the neutron

James Chadwick

Po

Be

n detector

detectorsource

No electric charge; mass ≈ proton mass

Nucleons (protons & neutrons)

proton neutron

mass 1.672x10-27kg 1.675x10-27kg

mc2 938.27 MeV 939.57 MeV

Charge +1.6x10-19 C 0

+

Isotopes

Same chemistry; very different nuclear physics

Light isotopes

AX

Chemical symbol

A = number ofprotons + neutrons

ZZ=# of protons

All elements have isotopes

238

92U

235

92U

Nuclear force

++

The very powerful electrical repulsion (100’s of Newtons)

must be counteractedby some other verystrong attractive

force

This new force is called the Strong Nuclear force

Strong Nuclear force

Forc

e

Distance (x10-15m) 1.0 2.0 3.0 4.0 5.0

Attractive nuclear force

repulsive electrical force

attraction isstronger here

repulsion isstronger here

Strong Nuclear Force

• It is very strong– It overcomes the electrical

repulsion between positively charged protons that are only 10-

15m apart.

• It acts over a very short range– It is not felt by nucleons when they

are more than 10-15m apart.

• It is selective– It is felt by neutrons & protons, but

not by electrons

Nuclei can’t be too large

+++

++

+

+

+

+

+

+

++

++

A proton feelselectrical repulsionfrom every protonin the nucleus

It feels a Strong Nuclearattraction only to nearby nucleons

In larger nuclei, the electricalforce is bigger while the nuclear force stays the same.

There are no stable nuclei above Z=82 (Lead)

+

+

++

++

+++

Eventually, the electrical repulsionoverwhelms the nuclear attraction

Discovery of radioactivity

Different types of radiation

Marie Curie

---

+++

neutral

- charged

+ charged

decayZY Z-2X + 2A A-4 4

Conservation of energy in decay

ZY Z-2X + 2A A-4 4

parent daughters

Energy of parent= Energy of daughters

Conserv. of energy in decay

ZY Z-2X + 2A A-4 4

parent daughters

v

= MXc2 + Mc2 + KEMYc2KE = MYc2 - MXc2 - Mc2

Energy balancepar

ent d

aughte

rs

the mass difference,times c2, becomes KE

KE = Mparentc2 – (Mdaughters c2)

-particle Kinetic Energy

Some mass is changed into Kinetic Energy

All the a particles havethe same Kinetic Energy

ZY Z+1X + e-A A

n p + e-

Beta () decay

+ e-

6C147N14

+

++

+

++ +

++

+

+

++7p

7n6p8n

88Ra 89Ac + e-228 228

Other beta decays

1H 2He + e-3 3

Tritium Beta decay

+ e-

3H 3He+ +

+

Energy balance in beta decay

14C160 keV

14N+e-

1 keV = 1000 eV

Electron energy in 14C beta decay

160 keV KEe-

KEe-

None of the electrons have160 keV of kinetic energy they all have less than that amount

What has happened to the “missing” energy??

Pauli’s “desperate solution”

no chargeno mass

Another “unseen” particle isemitted in decay process

6C 7N + e- + 14 14

14C decay revisited

e-6C14

7N14

1H 2He + e- + 3 3

3H decay revisited

e-3H 3He

Energy balance in beta decay

parent KEe- + KE

daughters

Cosmic gallNEUTRINOS, they are very small. They have no charge and have no mass And do not interact at all. The earth is just a silly ball To them, through which they simply pass, Like dustmaids down a drafty hall Or photons through a sheet of glass. They snub the most exquisite gas, Ignore the most substantial wall, Cold shoulder steel and sounding brass, Insult the stallion in his stall, And scorning barriers of class, Infiltrate you and me! Like tall and painless guillotines, they fall Down through our heads into the grass. At night, they enter at Nepal and pierce the lover and his lass From underneath the bed-you call It wonderful; I call it crass.

John Updike

Radioactive half-life

N = N0 ( ½ )n

Number ofremaining atoms

Initial numberof atoms number

of halflives

Some half-lives

3H (3He + e- + ) 12.3 yrs14C(14N + e- +) 5730 yrs238U(234Th +) 4.5x109 yrs235U(231Th + ) 7.1x108 yrs226Ra(222Rn + ) 1600 yrs28Mg(28Al + e- + ) 21 hrs213Po(209Pb + ) 4x10-6 s

T1/2

Carbon-14 dating

14C content

Shroud of Turin