1. CLRS 321 Nuclear Medicine Physics and Instrumentation 1
Unit I: Physics of Nuclear Medicine Lecture 2 Mass Energy Equivalence and Units
CLRS 321
Nuclear Medicine Physics and Instrumentation 1

2. Lecture Objectives
State the relationship of mass and energy in Einstein’s equation
Relate mass defect to nuclear binding energy
Recognize prefixes relating to different base-10 exponents and convert equivalent values between each
Identify the units of measurement used in nuclear medicine physics
Convert between conventional English and SI Units, particularly in regard to radioactivity and exposure

3. Mass Energy Equivalence (The Binding Energy of the Nucleus)
The positively charged protons and the neutral neutrons have specific binding energies that hold them together in the nucleus.
Paul Early, D. Bruce Sodee, Principles and Practice of Nuclear Medicine, 2nd Ed., (St. Louis: Mosby 1995), pg. 14.
A Helium atom is composed of two protons and two neutrons, plus a couple of electrons. Yet, the mass of two protons and two neutrons by themselves is more than the Helium nucleus (without the electrons). This is referred to as the mass defect. What’s behind it?
Some of the mass of the protons and neutrons is being converted into energy, according to Einstein’s famous equation:
E = mc2
This converted energy is the binding energy of the nucleus.

4. e⋅lec⋅tron-volt
  –noun Physics. a unit of energy, equal to the energy acquired by an electron accelerating through a potential difference of one volt and equivalent to × 10−19 joules. Abbreviation: eV, ev, Also, electron volt.
Origin: 1925–30
Dictionary.com Unabridged Based on the Random House Dictionary, © Random House, Inc
In the radiological sciences, we usually measure energy in kilo (i.e. 1000) electron Volts, or keV;
as well as Mega electron Volts (i.e. 1,000,000), or MeV.
electronvolt. (n.d.). Dictionary.com Unabridged (v 1.1). Retrieved August 22, 2009, from Dictionary.com website:

5. Converting the Mass of an Electron to Energy (from your textbook)
Rest mass of electron = 9.1 X 10-31kg
(Energy)
(Mass)
(Speed of Light Squared)

6. Converting Electron Mass Continued
We wanted our end unit in eV, but the unit we ended up with can is equivalent to a joule (joules can be converted to eV)
Therefore:

7. Converting Electron Mass Continued
Now we can convert joules to eV:
We apply this to our electron energy:
X 105 eV

8. Converting Electron Mass Continued
Often atomic-mass level energy is expressed in Mega electron Volts (MeV), which is equivalent to a million electron Volts. So We can convert our eV to MeV with the following:
Now we apply…
X 105
X 105 X

9. Converting Proton Mass to Energy (MeV)
We won’t go through all the steps, but basically:
Therefore, the energy equivalent of a proton’s mass is about 938 MeV

10. Converting Neutron Mass to Energy (MeV)
Therefore, the energy equivalent of a neutron’s mass is about 941 MeV

11. Mass Defect of the Carbon Nucleus (example)
AMUs were defined using the weight of a Carbon nucleus: 6 protons and 6 neutrons (12 nucleons)
A carbon atom nucleus = AMU
A proton = AMUs
A neutron = AMUs
Therefore, AMU is unaccounted for based on Carbon’s standard of 12 AMU
(Kahn Academy example: )

12. Mass Defect of the Carbon Nucleus (example)
This extra mass ( AMU) is converted to binding energy which is holding the nucleus together.
This difference is called the mass defect
AMUs are simply another unit of mass, and we can convert it to kg based on:
We will find the binding energy in class using E = mc2
1 AMU ≡ X kg

13. Common Exponent Values in Nuclear Medicine
Abbreviation
Prefix Name
Value
Common term value
Common Example p
pico-
10-12
one trillionth
pA (picoAmps) n
nano-
10-9
one-billionth
nm (nanometers)
micro-
10-6
one millionth
µCi (microCuries) m
milli-
10-3
one thousanth
mCi (milliCuries) c
centi-
10-2
one hundreth
cm (centimeters) k
kilo-
103
a thousand
keV (kilo electron Volts) M
Mega-
106
a million
MBq (Megabequerels) G
Giga-
109
a billion
GBq (Gigabequerels) T
Tera
1012
a trillion
TB (Terabyte)

14. Common Units in Nuclear Medicine
Measured Item
Common Old Unit
SI Unit
Conversion Factor
Radioactivity
milliCurie (mCi)
Megabequerels (Mbq)
1 mCi ≡ 37Mbq
Radiation Exposure (air kerma)
Roentgen (R)
Coulomb/kg
1 R ≡ 2.58 X 10-4 C/kg
Radiation Absorbed Dose
rad
Gray (Gy)
1 rad ≡ 0.01 Gy
Radiation Dose Equivalent
rem
Sievert (Sv)
1 rem ≡ 0.01 Sv
Distance
inch (in)
Centimeter (cm)
1 in ≡ 2.54 cm
Weight (mass)
pound (lb)
Kilogram (kg)
2.2 lb ≡ 1 kg

15. Homework 1 will be due in class, Monday, September 11th!
Next Time….
Modes of Radioactive Decay.
Homework 1 will be due in class, Monday, September 11th!