Nuclear Physics, JU, Second Semester, 2010-2011(Saed Dababneh).

1

Nuclear Size

Alpha particle (+2e)

Gold nucleus (+79e)d

Quite old!!!

Nuclear Physics, JU, Second Semester, 2010-2011(Saed Dababneh).

2

Nuclear Size• Closest approach “d”.• E = ECoulomb d = 2kZe2/E

• What about the recoil nucleus?• Show that

where mN : mass of the nucleus m : mass of alphaWhat are the values of d for 10, 20, 30 and 40 MeV on Au?How does this explain … ?

)(

2 2

mmE

mkZed

N

N

Nuclear Physics, JU, Second Semester, 2010-2011(Saed Dababneh).

3

Nuclear Shape• Crude Nucleons in the nucleus are confined to an approximately spherically symmetric structure Nuclear radius.• Deformations…! Consequences….!! Advanced models.

• HW 5HW 5If it is assumed that the charge is uniformly spherically distributed in a nucleus, show that the electric potential energy of a proton is given by:

R

eZZKE

2)1(

5

3

Nuclear Physics, JU, Second Semester, 2010-2011(Saed Dababneh).

4

Nuclear Mass• Nuclear masses measured to high accuracy:

• mass spectrograph.• energy measurement in nuclear reactions.

B

Ev

qvBqE

E

rqB

v

qBrm

qB

mvr

qrBmv

qvBr

vm

2

2

If same B.

Absolute measurement

Nuclear Physics, JU, Second Semester, 2010-2011(Saed Dababneh).

5

• m(12C) = 12 u. m(1H) with high precision?• Relative measurement. Mass Doublet method.• Mass 128. Difference in mass between C9H20 and C10H8 = 0.093900320.00000012 u = 12m(1H) – m(12C) • m(1H) = 1.00782503 0.00000001 u.

• Usually atomic masses are tabulated.http://physics.nist.gov/cgi-bin/Compositions/stand_alone.pl?ele=&all=all&ascii=ascii&isotype=all

• Mass of the atom < ZmH + Nmn. Why?• Mass decrement = difference between actual mass and mass number: Δ = m – A• Δ could be positive or negative.

Nuclear Mass

Nuclear Physics, JU, Second Semester, 2010-2011(Saed Dababneh).

6

Nuclear Binding Energy Btot(A,Z) = [ ZmH + Nmn - m(A,Z) ] c2 Bm

Bave(A,Z) = Btot(A,Z) / A

Separation Energy Neutron separation energy: (BE of last neutron)Sn = [ m(A-1,Z) + mn – m(A,Z) ] c2

= Btot(A,Z) - Btot(A-1,Z) Prove that Sp = [ m(A-1,Z-1) + m(1H) – m(A,Z) ] c2

= Btot(A,Z) - Btot(A-1,Z-1) Prove thatS = ??

HW 6HW 6 Krane 3.9, 3.12, 3.13 and 3.14.

Magicnumbers

Nuclear Physics, JU, Second Semester, 2010-2011(Saed Dababneh).

7

Nuclear Binding Energy

Magicnumbers

Nuclear Physics, JU, Second Semester, 2010-2011(Saed Dababneh).

8

Nuclear Binding EnergyIn generalX Y + aSa(X) = (ma + mY –mX) c2

= BX –BY –Ba The energy needed to remove a nucleon from a nucleus ~ 8 MeV average binding energy per nucleon (Exceptions???).

Nuclear Reactionsa + X > Y + b or X(a,b)YQ-value = [m(a) + m(X) – m(Y) –m(b)] c2

Solve problem 11.6 in Krane.

Nuclear Physics, JU, Second Semester, 2010-2011(Saed Dababneh).

9

Nuclear Binding Energy

Fission

Fusi

on