Physics 12 Mr. Jean May 20th, 2014
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Physics 12
Mr. Jean
May 20th, 2014
The plan:
• Video clip of the day
• Question #1– Visiting the Relatives
• Binding energy
• Energy Deflection
• Mass and energy
Chapter 20: Introduction
• The Nucleus & Radioactivity:– Nuclear Mass
• P. 898
– Nuclear Energy• P. 902
– Radio Activity• P. 906
VERY IMPORTANT:
Atomic Mass Unit, uOne atomic mass unit (1 u) is equal to One atomic mass unit (1 u) is equal to one-twelfth of the mass of the most one-twelfth of the mass of the most abundant form of the carbon atom--abundant form of the carbon atom--carbon-12.carbon-12.Atomic mass unit: 1 u = 1.6606 x 10-
27 kgCommon atomic masses:
Proton: 1.007276 u
Neutron: 1.008665 u
Electron: 0.00055 u
Hydrogen: 1.007825 u
Example 1: The average atomic mass of Boron-11 is 11.009305 u. What is the mass of
the nucleus of one boron atom in kg?
Electron: Electron: 0.00055 u0.00055 u
115B = =
11.00930511.009305The mass of the nucleus is the atomic The mass of the nucleus is the atomic mass less the mass of Z = 5 electrons:mass less the mass of Z = 5 electrons:
Mass = 11.009305 u – 5(0.00055 Mass = 11.009305 u – 5(0.00055 u)u)1 boron nucleus = 11.00656 1 boron nucleus = 11.00656
uu-271.6606 x 10 kg
11.00656 u1 u
m
m = 1.83 x 10-26
kgm = 1.83 x 10-26
kg
2 8; 3 x 10 m/sE mc c 2 8; 3 x 10 m/sE mc c
Mass and EnergyRecall Einstein’s equivalency formula for m Recall Einstein’s equivalency formula for m
and E:and E:
The energy of a mass of 1 u can be The energy of a mass of 1 u can be found:found:
EE = (1 u) = (1 u)cc22 = = (1.66 x 10(1.66 x 10-27 -27 kg)(3 x 10kg)(3 x 1088 m/s)m/s)22
E = 1.49 x 10-10 J OrOr E = 931.5 MeV
When When converting amu converting amu
to energy:to energy:
2 MeVu931.5 c 2 MeV
u931.5 c
Example 2: What is the rest mass energy of a proton (1.007276 u)?
EE = = mcmc22 = = (1.00726(1.00726 u)(931.5 u)(931.5 MeV/u)MeV/u)
Proton: E = 938.3 MeVProton: E = 938.3 MeV
Similar conversions show Similar conversions show other rest mass energies:other rest mass energies:
Electron: Electron: EE = 0.511 = 0.511 MeVMeVElectron: Electron: EE = 0.511 = 0.511 MeVMeV
Neutron: E = 939.6 MeVNeutron: E = 939.6 MeV
The Mass DefectThe mass defect is the difference The mass defect is the difference
between the rest mass of a nucleus between the rest mass of a nucleus and the sum of the rest masses of its and the sum of the rest masses of its
constituent nucleons.constituent nucleons.
The mass defect is the difference The mass defect is the difference between the rest mass of a nucleus between the rest mass of a nucleus
and the sum of the rest masses of its and the sum of the rest masses of its constituent nucleons.constituent nucleons.
The whole is less than the sum of the The whole is less than the sum of the parts!parts! Consider the carbon-12 atom Consider the carbon-12 atom
(12.00000 u):(12.00000 u):Nuclear mass = Mass of atom – Electron Nuclear mass = Mass of atom – Electron
masses = 12.00000 u – masses = 12.00000 u – 6(0.00055 u) = 11.996706 6(0.00055 u) = 11.996706 uuThe The nucleusnucleus of the carbon-12 atom has this of the carbon-12 atom has this
mass.mass. (Continued . . .)(Continued . . .)
Mass Defect (Continued)Mass of carbon-12 nucleus: Mass of carbon-12 nucleus: 11.99670611.996706
Proton: 1.007276 Proton: 1.007276 uu
Neutron: 1.008665 Neutron: 1.008665 uu
The nucleus contains 6 protons and 6 The nucleus contains 6 protons and 6 neutrons:neutrons:
6 p = 6(1.007276 u) = 6.043656 u6 p = 6(1.007276 u) = 6.043656 u
6 n = 6(1.008665 u) = 6.051990 u6 n = 6(1.008665 u) = 6.051990 u
Total mass of parts: = Total mass of parts: = 12.095646 u12.095646 uMass defect Mass defect mmDD = 12.095646 u – = 12.095646 u –
11.996706 u11.996706 umD = 0.098940 u
mD = 0.098940 u
The Binding Energy
The binding energy The binding energy EEBB of a nucleus is of a nucleus is the energy required to separate a the energy required to separate a nucleus into its constituent parts.nucleus into its constituent parts.
The binding energy The binding energy EEBB of a nucleus is of a nucleus is the energy required to separate a the energy required to separate a nucleus into its constituent parts.nucleus into its constituent parts.
EB = mDc2 where c2 = 931.5 MeV/u
The binding energy for the carbon-12 The binding energy for the carbon-12 example is:example is:
EEBB = (= (0.098940 u)(931.5 MeV/u)
EB = 92.2 MeVBinding EB for C-12:
Binding Energy per Nucleon
An important way of comparing the nuclei An important way of comparing the nuclei of atoms is finding their binding energy per of atoms is finding their binding energy per
nucleon:nucleon:
An important way of comparing the nuclei An important way of comparing the nuclei of atoms is finding their binding energy per of atoms is finding their binding energy per
nucleon:nucleon:
Binding energy per
nucleon
MeV =
nucleonBE
A
For our C-12 example A = 12 and:For our C-12 example A = 12 and:
MeVnucleon
92.2 MeV7.68
12BE
A MeV
nucleon
92.2 MeV7.68
12BE
A
Formula for Mass DefectThe following formula is useful for mass The following formula is useful for mass
defect:defect:
D H nm Zm Nm M D H nm Zm Nm M Mass Mass
defectdefect mmDD
mmHH = 1.007825 u; m = 1.007825 u; mnn = 1.008665 = 1.008665 uuZ is atomic number; N is neutron Z is atomic number; N is neutron number; M is mass of atom (including number; M is mass of atom (including
electrons).electrons).By using the mass of the hydrogen atom,
you avoid the necessity of subtracting electron masses.
By using the mass of the hydrogen atom, you avoid the necessity of subtracting
electron masses.
Example 3: Find the mass defect for the nucleus of helium-4. (M = 4.002603 u)
D H nm Zm Nm M D H nm Zm Nm M Mass Mass
defectdefect mmDD
ZmZmHH = (2)(1.007825 u) = 2.015650 u = (2)(1.007825 u) = 2.015650 u
NmNmnn = (2)(1.008665 u) = 2.017330 u = (2)(1.008665 u) = 2.017330 u
MM = 4.002603 u (From nuclide tables) = 4.002603 u (From nuclide tables)
mmDD = (2.015650 u + 2.017330 u) - = (2.015650 u + 2.017330 u) - 4.002603 u 4.002603 u
mD = 0.030377 u
mD = 0.030377 u
42He
Example 3: Find the binding energy per nucleon for helium-4. (mD = 0.030377 u)
EB = mDc2 where c2 = 931.5 MeV/u
EB = mDc2 where c2 = 931.5 MeV/u
EEBB = = (0.030377 u)(931.5 MeV/u) = (0.030377 u)(931.5 MeV/u) = 28.3 28.3 MeVMeV
MeVnucleon
28.3 MeV7.07
4BE
A MeV
nucleon
28.3 MeV7.07
4BE
A
A total of 28.3 MeV is required To tear apart the nucleons from the He-4 atom. A total of 28.3 MeV is required To tear
apart the nucleons from the He-4 atom.
Since there are four nucleons, we find Since there are four nucleons, we find thatthat
Binding Energy Vs. Mass Number
Mass number A
Bin
din
g E
nerg
y p
er
nucl
eon
50
100 150
250
200
2
6
8
4
Curve shows Curve shows that that EEBB increases with increases with AA and peaks at and peaks at AA = 60 = 60. Heavier . Heavier nuclei are less nuclei are less stable. stable. Green region is Green region is for most stable for most stable atoms.atoms.
For heavier nuclei, energy is released when For heavier nuclei, energy is released when they break up (they break up (fissionfission). For lighter nuclei, ). For lighter nuclei, energy is released when they fuse together energy is released when they fuse together ((fusionfusion).).
To do:
• P. 902– Questions 1, 2 & 3
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